Journal of Sensors

Volume 2019, Article ID 4581672, 14 pages

https://doi.org/10.1155/2019/4581672

## A Deep Learning Model for Concrete Dam Deformation Prediction Based on RS-LSTM

^{1}Institute of Water Resources and Hydro-Electric Engineering, Xi’an University of Technology, Xi’an 710048, China^{2}Department of Development, Sino Hydro Engineering Bureau 15 Co., Ltd, Xi’an 710016, China

Correspondence should be addressed to Xudong Qu; nc.ude.tuax.uts@dxq

Received 23 June 2019; Accepted 14 September 2019; Published 31 October 2019

Guest Editor: Samir Mustapha

Copyright © 2019 Xudong Qu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Deformation is a comprehensive reflection of the structural state of a concrete dam, and research on prediction models for concrete dam deformation provides the basis for safety monitoring and early warning strategies. This paper focuses on practical problems such as multicollinearity among factors; the subjectivity of factor selection; robustness, externality, generalization, and integrity deficiencies; and the unsoundness of evaluation systems for prediction models. Based on rough set (RS) theory and a long short-term memory (LSTM) network, single-point and multipoint concrete dam deformation prediction models for health monitoring based on RS-LSTM are studied. Moreover, a new prediction model evaluation system is proposed, and the model accuracy, robustness, externality, and generalization are defined as quantitative evaluation indexes. An engineering project shows that the concrete dam deformation prediction models based on RS-LSTM can quantitatively obtain the representative factors that affect dam deformation and the importance of each factor relative to the effect. The accuracy evaluation index (AVI), robustness evaluation index (RVI), externality evaluation index (EVI), and generalization evaluation index (GVI) of the model are superior to the evaluation indexes of existing shallow neural network models and statistical models according to the new evaluation system, which can estimate the comprehensive performance of prediction models. The prediction model for concrete dam deformation based on RS-LSTM optimizes the factors that influence the model, quantitatively determines the importance of each factor, and provides high-performance, synchronous, and dynamic predictions for concrete dam behaviours; therefore, the model has strong engineering practicality.

#### 1. Introduction

Due to unique advantages in design, construction, and operational management, concrete dams account for a large proportion of all dams and have become the preferred dam type for the construction of high dams. However, most of the concrete dam projects are located in harsh alpine valleys. Thus, the dams are subjected to various dynamic, static, and special cyclic loads during service, and the design, construction, and operational management must be tailored to these conditions. Therefore, service safety behaviour involves a nonlinear dynamic process that includes material and structure interactions and multiple factors [1]. As a comprehensive variable that reflects the safety state of concrete dams, deformation can be used as an important index of structural behaviours and trends. Therefore, strengthening the prediction models for deformation, conducting safety monitoring, and establishing early warning systems are important ways to ensure long-term service safety of concrete dams [2].

In recent years, the successful application of dam engineering theory, finite element theory, and artificial intelligence (AI) technology has greatly promoted the development of concrete dam deformation prediction models. The most commonly used methods [3] for influential factor selection in concrete dam deformation prediction models include prior knowledge, linear correlation coefficient, stepwise regression, principal component analysis (PCA), and grey correlation analysis methods. However, in actual applications, the prior knowledge method relies too much on experience and has large errors. Notably, the water pressure, temperature, and dam age are generally selected as influential factors in hydrostatic seasonal temporal (HST) models considering simplified physical models of dams and dam foundations, the burial conditions of monitoring equipment, prototype monitoring data, engineering mechanical analysis, and deductive investigation. The limitation of the PCA method is that only linear relations between variables are considered. If the dependence is nonlinear, the misinterpretation of results may occur. The grey correlation analysis method can only sort factors according to their relevance, and there is no clear criterion for selecting influential factors. Moreover, multiple collinearity can exist among the factors selected by conventional methods, which may reduce the accuracy of the model and adversely affect the prediction results [4]. Meanwhile, prediction models do not consider the influence of nonquantitative factors such as the seepage flow, crack opening degree, and lifting pressure; the dam construction materials; the construction quality; and the geological conditions. Additionally, model interpretation is important for evaluating the performance of prediction models, especially the model accuracy. The HST model has been traditionally used to identify the response of a dam to a considered action, such as a hydrostatic load, or to variations in factors such as temperature and time [5]. However, such analyses are only valid if the predictor variables are independent, which is not generally true [6]. In contrast, intelligent models (such as neural network, multilayer perceptron, and support vector machine models) have not been applied to interpret dam behaviour. Traditional models are frequently termed “black box” models, in reference to their lack of interpretability. Therefore, in the selection process of the factors that influence concrete dam deformation prediction models, imperfect selection criteria and neglecting important factors can seriously affect the prediction performance of the model. Single-point statistical models, deterministic models, and hybrid models [7–10] have evolved into multipoint intelligent models [11–16]. Based on the traditional statistical model, Gu et al. treated deformation at multiple measurement points and the spatial coordinates of these points as variables and established a spatiotemporal distributed prediction model of the deformation field of a concrete dam. Li et al. investigated the spatial and temporal expression of the factors that affected the deformation of an RCC dam and established a spatiotemporal deformation prediction model for RCC dams based on measured data. The prediction results agreed to the actual dam deformation data. Li et al. used the strong functional nonlinear mapping ability of a back propagation (BP) neural network to replace the complex factor subset in the traditional spatial deformation field model with water level, temperature, time, and measurement point variables as the input of the neural network. A BP network prediction model was established for dam deformation at multiple points. Chen et al. proposed a spectral decomposition method to decompose the monitoring data collected at multiple measurement points into several mutually independent latent variables for noise reduction and monitoring data processing. A least square support vector machine prediction model was established between the environmental data and latent variables, and the horizontal displacement of Mianhuatan Dam was successfully predicted. Many scholars have addressed these issues. The successful application of new methods has expanded the theoretical knowledge of dam deformation prediction and model establishment and provided important guiding significance for engineering practice. However, due to the complexity of concrete dam engineering, the structural volatility of dams, and the uncertainty of working conditions, there are still some shortcomings in existing prediction models. It is difficult for some models to process massive amounts of monitoring data in real time with extensive mining data mechanisms for high-performance prediction targets, such as those in practical applications. It is important to appropriately evaluate the prediction performance of a model from all angles because the practical value of the models can be guaranteed, different models can be compared, and different warning thresholds can be defined. There are various indexes [17] that can be used to assess how well a model matches the observed data, among which the most commonly used are the mean squared error (MSE), root mean squared error (RMSE), coefficient of determination (), mean absolute error (MAE), mean absolute percentage error (MAPE), and average relative variance (ARV). The result of any of these indexes is frequently equivalent to a given prediction task. Specifically, an accurate model will have small MSE, RMSE, MAE, and MAPE values and high and ARV values. However, these accuracy indexes have differences that can be relevant but are often not considered [18]. Commonly, robustness and generalization ability are neglected in the model assessment, and quantitative evaluation indexes are not always used in practical applications. Therefore, it is necessary to explore methods for factor selection, establish high-performance, dynamic, synchronous prediction models, and design a scientific and comprehensive evaluation system which are urgent for concrete dam deformation prediction.

Attribute reduction is one of the core concepts of RS theory, which addresses incompleteness, redundancy, and ambiguity in data in the field of machine learning. This approach avoids the use of complex discernibility matrices and uses attribute importance as heuristic information to obtain inductive sets and importance analysis results; excellent results can be obtained in factor selection for prediction models based on RS theory [19–21]. Moreover, long short-term memory (LSTM) based on the memory architecture in deep learning (DL) can overcome the memory shortage and vanishing gradient issues of recurrent neural networks (RNNs). Besides, this method is characterized by controllable memory and rapid convergence. LSTM has achieved good practical application results in the dynamic and deep processing of massive, long-term, dependent data series [22–25]. To overcome the shortcomings of existing concrete dam deformation prediction models, RS theory and an LSTM network are applied to a concrete dam deformation prediction model in virtue of Tensor Flow. Finally, a concrete dam deformation prediction model based on RS-LSTM is established, and a new predictive model evaluation system is proposed.

#### 2. Materials and Methods

##### 2.1. Rough Set Theory

RS theory was proposed by Polish scholar Pawlak in the 1980s. The core objectives are the mining and refining of essential information under the premise of maintaining equivalence relations. The main tasks in this approach are attribute reduction, correlation analysis, and importance evaluation for uncertain information systems.

###### 2.1.1. Information System

To describe the samples that encompass the necessary information in RS theory, a quaternary information system is established, and it can be expressed as follows: where is a nonempty finite set of all samples; is a set of attributes, including a set of conditional attributes and a set of decision attributes ; is the attribute value set; and is the information function, also known as the decision table.

###### 2.1.2. Attribute Reduction

For arbitrary and , the indistinguishable relationship between and is defined as follows.

For an arbitrary set of objects and attributes in a given information system , the approximation of is defined as ; the approximate definition of is defined as ; and the boundary area of is defined as . In this case, represents the set of indistinguishable relations for the division of by .

If is not empty, then is called a rough set of . The positive region of relative to is as follows.

When , where , can be omitted. Additionally, when each element in is not omissible from , it can be concluded that is independent of . When , where is independent of and all the elements in can be omitted, then is called the relative reduction of .

###### 2.1.3. Importance Evaluation

In attribute reduction, the importance of the attribute can be defined by the degree of interdependence between the attribute sets and . The degree of interdependence between and is defined as follows: where represents the cardinality value of a set.

The importance of the conditional attribute to the decision attribute based on the attribute dependency degree is defined as follows.

##### 2.2. LSTM Network Based on a Memory Architecture

LSTM is obtained by improving the hidden layer of the RNN structure. LSTM based on a memory architecture can overcome memory shortage and vanishing gradient problems. The LSTM model structure is shown in Figure 1. The key advantages of LSTM are twofold. Notably, the hidden layer includes a hidden state and a cell state, and a threshold mechanism is established in the RNN. These factors strengthen the ability of the model to learn current information, extract the information and rules associated with the data, and simultaneously transmit information to reduce memory use. The threshold mechanism uses input gates, forget gates, and output gates to selectively memorize the feedback parameters of the feedback error function as the gradient decreases, achieving rapid gradient convergence [26].