Deformation forecasting of a hydropower dam by hybridizing a long short-term memory deep learning network with the coronavirus optimization algorithm

DOI: 10.1111/mice.12810 ORIGINAL ARTICLE Deformation forecasting of a hydropower dam by hybridizing a long short-term memory deep learning network with the coronavirus optimization algorithm Kien-Trinh T. Bui1José F. Torres2David Gutiérrez-Avilés2 Viet-Ha Nhu3Dieu Tien Bui4Francisco Martínez-Álvarez2 1Faculty of Water Resources Engineering, Thuyloi University, Hanoi, Vietnam 2Data Science and Big Data Lab, Pablo de Olavide University, ES-41013 Seville, Spain 3Department of Geological-Geotechnical Engineering, Hanoi University of Mining and Geology, Hanoi, Vietnam 4GIS Group, Department of Business and IT, University of South-Eastern Norway, Bø i Telemark, Norway Correspondence Kien-Trinh T. Bui,Faculty ofWater ResourcesEngineering,ThuyloiUniversity,Hanoi,Vietnam Email:[email protected] FranciscoMartínez-Álvarez,DataScienceandBig Data Lab,PablodeOlavide University,ES-41013Seville,Spain. Email:[email protected] Fundinginformation VietnamNationalFoundation for Science andTechnology Development (NAFOSTED),GrantNumber:105.08-2018.06; SpanishMinistryof Science, Innovation andUniversitiesunder project,Grant Number:PID2020-117954RB-C21. https://doi.org/10.1111/mice.12810 Abstract The safety operation and management of hydropower dam play a critical role in social-economic development and ensure people’s safety in many countries; therefore, modeling and forecasting the hydropower dam’s deformations with high accuracy is crucial. This research aims to propose and validate a new model based on deep learning long short-term memory (LSTM) and the coronavirus optimization algorithm (CVOA), named CVOA-LSTM, for forecasting the deformations of the hydropower dam. The second-largest hydropower dam of Vietnam, located in the Hoa Binh province, is focused. Herein, we used the LSTM to establish the deformation model, whereas the CVOA was utilized to optimize the three parameters of the LSTM, the number of hidden layers, the learning rate, and the dropout. The efficacy of the proposed CVOA-LSTM model is assessed by comparing its forecasting performance with state-of-the-art benchmarks, sequential minimal optimization for support vector regression, Gaussian process, M5’ model tree, multilayer perceptron neural network, reduced error pruning tree, random tree, random forest, and radial basis function neural network. The result shows that the proposed CVOA-LSTM model has high forecasting capability (R2=0.874, root mean square error =0.34, mean absolute error =0.23) and outperforms the benchmarks. We conclude that CVOA-LSTM is a new tool that can be considered to forecast the hydropower dam’s deformations. 1 INTRODUCTION Dam safety has a large effect on many aspects of life, such as life safety, property, and the dam’s ecological environment; therefore, safety monitoring is an essential part of the dam management system (Salazar et al., 2017;Tuetal., 2013;R.T.Wuetal.,2019). The primary purpose of safety monitoring is to detect abnormal movements on the surface or inside the dam to take appropriate and timely remedies. Because of the nonlinear and complex characteristics of dam movement, it is ©2022 Computer-Aided Civil and Infrastructure Engineering still challenging for the managers to forecast this displacement process with high accuracy (De Sortis & Paoliani, 2007; Mata, 2011; Salazar et al., 2015). Forecasting and diagnosing deformations of hydropowerdam basedon timeseriesmonitoring dataplay an essential role in dam safety assessment and risk management, especially with hydropower dams constructed more than 40 years ago, where the technology and computational tool used were limited (Hariri-Ardebili & Salazar, 2020). In this regard, the forecasting accuracy of deformations is highly necessary for issuing crucial decisions. Comput Aided Civ Inf. 2022;1–19. wileyonlinelibrary.com/journal/mice 1 2BUI ET AL. During the last 5 years, long short-term memory (LSTM) has received significant attention in time-series forecasting and analysis due to its outstanding performance in various domains (Du et al., 2020;Y.Lietal.,2020). However, designing LSTM for the deformation forecasting of hydropower dam is still challenging because it requires adapting and optimizing various parameters. Herein, we formulate the deformation forecasting as a multivariate time-series regression. The inputs are factors related to the upstream water level (UpL), the downstream water level, the air temperature, and the dam’s age; the output is the horizontal deformation (HD). Nevertheless, designing accurate LSTM models is a difficult task because the performance of LSTM is very sensitive with the hidden layer amount and the parameters employed, and they should be determined objectively. Additionally, LSTM has two major drawbacks: First, the execution time is very high, and second, the model is quite sensitive to its hyperparameters adjustment. For these reasons, it is of utmost relevance to be able to train the deep learning models with the optimal values for the hyperparameters. This is typically done by means of optimization methods or metaheuristics, highlighting those based on bioinspired phenomena (Alba et al., 2013). This hybridization usually leads to optimized deep learning models with high performance, which is a very hot topic in the literature nowadays. In this research, we partly fill this gap by proposing a new approach for forecasting the deformation of hydropower dam using deep learning LSTM (Lara-Benítez et al., 2020; Torres et al., 2021) optimized by the coronavirus optimization algorithm (CVOA) and named as CVOA-LSTM. The CVOA is a new optimization introduced by Martínez-Álvarez et al. (2020) that mimics the development and spread of the Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2), responsible for the coronavirus disease 2019 (COVID-19). The purpose of the CVOA here is to search and optimize the LSTM, aiming to forecast the deformation with high accuracy. The effectiveness of the proposed LSTM-CVOA hybrid model has been used for forecasting the deformation monitoring data at the Hoa Binh hydropower dam of Vietnam, the second-largest dam in Southeast Asia. LSTMCVOA is compared with benchmark algorithms, that is, support vector regression optimized by the sequential minimal optimization (SMO-SVR), Gaussian process (GP), M5 model tree (M5’), multi-layer neural network (MLPNeuralNet), reduced error pruning decision tree (REPTree), random tree (RT), random forest (RF), and radial basis function neural network (RBFNeuralNet). The popular hydrostatic-season-time (HST) model for dam monitoring has also been used as a baseline. Furthermore, different CVOA is compared to different optimization strategies such as grid search (GS), random search (RS), and genetic algorithms, showing better performance for all the compared cases. The rest of the paper is structured as follows. Section 2 discusses related works. The underlying foundations of the methods used are introduced in Section 3. Section 4 presents the case study. Section 5details how the proposed methodology has been applied to the case-study data. Section 6reports the results achieved and discusses them. Finally, conclusions, limitations, and future works are summarized in Section 7. 2 RELATED WORKS Various methods have been proposed for forecasting and analyzing the dam displacement, and they could be categorized as deterministic group, statistical group, and machine learning methods (Salazar et al., 2017). Based on the definition, the deterministic group refers to the physical models, but physical models do not necessarily need to be deterministic. In fact, they can be used as a simulation tool in a probabilistic assessment. For example, the input uncertainties can be quantified, sampled, and propagated through the simulation model to generate probabilistic outputs. In addition, one could also conduct simulation optimization. Deterministic methods are well-known as the finite element method (Gurbuz, 2011; Pereira et al., 2020), boundary element method (Antes & Von Estorff, 1987). In these methods, parameters/quantities related to structures, such as material, stress-strain, seepage, are employed to establish mathematical functions to relate the dam’s displacement over time. Therefore, they are commonly used in the damdisplacementanalysis at theconstructingand first filling phases. When the monitoring time-series data is long enough, statistical methods, that is, hydrostatic–seasonal–time (Sigtryggsdóttir et al., 2018), have more advantages than deterministic methods in terms of more straightforward function form and calculating speed (Shao et al., 2017;Stojanovic et al., 2013; Wei et al., 2020). However, in some cases, it is impossible to obtain enough time-series data, so the reliability of the methods is not guaranteed. Besides, as we know, dam deformation is a typical nonlinear process, so it is difficult for statistical methods to forecast with high accuracy (Salazar et al., 2015). Recently, machine learning, that is, neural networks (Kao & Loh, 2013; Mata, 2011; Ranković et al., 2012; Rodríguez et al., 2019; Salazar et al., 2017), artificial immune algorithm (Xi et al., 2011), support vector machine (SVM; Ranković et al., 2014; Salazar et al., 2015;Suetal., 2017; Tabari & Sanayei, 2018; Wei et al., 2020; Zheng BUI ET AL. 3 et al., 2013), wavelet SVM (Su et al., 2018), RF and boosted regression tree (Salazar et al., 2016), GP (Kang & Li, 2020), multivariate adaptive regression splines (Salazar et al., 2015), adaptive neural fuzzy inference system (Bui et al., 2018; Ranković et al., 2012; Taormina & Chau, 2015), multiblock-based diagnosis method (Qin et al., 2017), and signalresidual amendment (Wei et al., 2020), have successfully forecasted dam displacement with great accuracy results. More recently, recurrent neural networks (RNN) and variants like LSTM networks, introduced by Hochreiter and Schmidhuber (1997), have received great attention in solving regression problems in various engineering fields (Chen et al., 2020; Hua et al., 2019;Nietal.,2020;Ni et al., 2020; Divina et al., 2020; Torres et al., 2018; Torres, Troncoso, et al., 2019; Zhang et al., 2019). Moreover, much attention has been paid to the optimization of such models, which are quite sensitive to the parameters setting (Charte et al., 2020; Siqueira et al., 2020; Thurnhofer-Hemsi et al., 2020). Ribeiro et al. (2019) compared Seasonal Autoregressive Integrated Moving Average (SARIMA), Seasonal Autoregressive Integrated Moving Average Exogenous model (SARIMAX), and a hybrid SARIMAX-LSTM for forecasting the concrete dam’s displacements with a report that the hybrid model is capable of providing a better forecast accuracy. Yang et al. (2020) employed LSTM to predict a concrete dam’s deformation with good results (Rafiei et al., 2017;Rafieiand Adeli, 2017). Y. Li et al. (2020)proposedanensembleof the Loess-based seasonal-trend decomposition, extra trees, and LSTM for analyzing the displacements of a concrete dam with outstanding forecasting performance. Liu et al. (2020) consider the integration of the moving average technique, principal component analysis, and LSTM for predicting displacements of arch dams with a conclusion that the LSTM-MA delivers better prediction results. Overall, though these machine learning algorithms require long time-series data, they are potent tools in nonlinear process relationships of the dam displacement and influence of external factors. Nevertheless, there is no consensus on which machine algorithm is the best for forecasting deformations of dams. As a result, the exploration and development of new algorithms to improve forecasting capability is still an essential issue in dam deformation analysis. 3CASE STUDY 3.1 Overview of the hydropower dam In this research, a hydropower dam located in the Da river section flowing through the Hoa Binh city in northwest Vietnam was adopted as a case study (see Figure 1). This is the second largest hydroelectric project in Southeast Asia after the Son La hydropower plant in the north of Vietnam that was completed in 2012. The hydropower project, which was designed, supplied equipment, and constructed by the former Soviet Union started on November 6, 1979, and was completed on December 20, 1994 (Vladimirov et al., 2003). The project consists of eight hydroelectric generators with a total capacity of 1920 MW, and they were located in the underground of an effusive rock hill, which can suffer from seismic and earthquakes up to Level 8 (Ezersky & Eppelbaum, 2017; Ezerskii et al., 1990). In the first period of the operation, the electricity production accounted for about 40% of the total production in Vietnam, and during the last 26 years, this project has produced about 230 billion kWh. Besides the power supply, the project’s other primary function is to regulate and control floods to ensure safety for both the Hanoi capital and the Red River Delta provinces, where the total population is more than 22.5 million people in 2019 (GSO, 2020). This project’s dam was constructed from 1981 to 1990, and this is the clay core-based rock-earth fill dam with a length and height of 734 and 128 m, respectively. The highest water level is designed at 120 m, whereas the lowest level is 80 m. The dam can withstand the highest difference in height between the upstream and the downstream water levels of 102 m. The monitoring data at the dam showed that the difference in the water flow between the dry and flood seasons is large. For example, in 1971, a recorded flow in the dry season is 600 m3/s, and the flood season is up to 14800 m3/s. It should be noted that the total reservoir area is around 208 km2, and the total water storage volume is 9.45 billion m3. 3.2 Health monitoring data To monitor the dam behavior, a geodetic network with 12 points has been established on the downstream face, in which 6 points (PV2, PV4, PV6, PV8, PV10, PV12) have been placed at 123 m high, whereas the six remaining points (PV1, PV3, PV5, PV7, PV9, PV11) have setup at 75 m high. The horizontal movement of those points was measured and determined using a triangular geodetic network measured. Therein, theodolites were used for the measurement before the year 2000, and then, total stations have been replaced and used for the measurement until now. In this analysis, the HD data measured at the PV6 point in around 22 years, from January 23, 1998, to September 5, 2019, were considered. The PV6 point was selected because it is located near the middle of the dam (123 m high). 4BUI ET AL. FIGURE 1 Hoa Binh hydropower dam: (a) Location of the dam; (b) the dam view from the google earth; (c) the dam from the downstream view; and (d) the dam from the upstream view (photo courtesy of Ngoc Thanh) TABLE 1 A statistical overview of the time-series data for the horizontal deformation (HD) analysis in this research No. Variable Unit Min Max Mean Std. error Std. dev 1 HD m 0.088 0.199 0.121 0.001 0.022 2Upstream water level m78.56 117.25 104.92 0.64 10.38 3 Downstream water level m 9.65 21.65 13.53 0.13 2.16 4Air temperature Degree 12.40 32.30 24.37 0.29 4.72 5 Dam age Month 92.47 355.63 222.45 4.77 76.95 Together with the HD data, other related time-series data were monitored, including UpL, downstream water level (DoL), air temperature (t), and the dam age in month (θ) were also considered. The statistical description of the monitoring data used in this analysis is shown in Table 1 and graphical presentations of these data are shown in Figure 2. According to the report of Hoa Binh hydropower company, from the year 2005, TCA2003 of Leica (precision of 0.5″ for horizontal displacement angular and 1 mm + 1 ppm/0.3 s for distance) was used to measure the 31 angles and 28 distances in the monitoring network. After adjusting the computation of each monitoring epoch, the coordinates and position of all monitoring points are determined inaccuracy of 1 mm or below. Thus, this value also is the accuracy of individual value in each monitoring epoch and is chosen as the standard error of dam horizontal displacement time-series in Table 1. BUI ET AL. 5 FIGURE 2 Time series monitoring data: (a) horizontal deformation (HD; m) at the PV6 station and (b) air temperature (o) 4BACKGROUND OF THE EMPLOYED ALGORITHM This section provides the necessary theoretical information for a better understanding of the proposed approach. Thus, Section 4.1 introduces the LSTM network and Section 4.2, the CVOA, used to optimize the deep learning model hyperparameters. 4.1 LSTM networks This section describes the mathematical foundations underlying the LSTM network. LSTMs are RNN architectures used in deep learning. Such architecture is particularly suitable to process images, video, or speech, leading to successful applications in civil and infrastructure engineering (Jeong et al., 2020; Jiang & Zhang, 2020;F.Nietal., 6BUI ET AL. 2019;Xuetal.,2020). However, it can also be applied to the field of time-series forecasting, as widely discussed in the literature, given their ability to deal with lags of arbitrary duration. Standard RNNs suffer from gradient issues, which consists of decreasing the gradient as the number of layers increases. Actually, for RNNs with a high number of layers, the gradient becomes almost null, preventing the network from learning. For this reason, these networks have a short-term memory and do not obtain good results when dealing with long sequences that require memorizing all the information contained in the complete sequence. LSTM recurrent networks have emerged to solve the vanishing gradient problem (Hochreiter et al., 1997), using three gates to keep longstanding relevant information and discard irrelevant information. These gates are: 1. Forget gate, Γf. It decides the information that should be discarded or saved. A value near to 0 means that the past information is forgotten, while a value near 1 means that it is kept. 2. Update gate, Γu. It decides which new information ctto use to update the ctmemory state. Thus, ctis updated using both Γfand Γu. 3. Output gate, Γo. It decides which is the output value that will be the input of the next hidden unit. The information of the at−1previous hidden unit and the information of the xtcurrent input is passed through the sigmoid activation function, σ, to compute all the gate values and through the tanh activation function to compute the ctnew information, which will be used to update the values. The equations defining an LTSM unit are: 𝑐𝑡=tanh (𝑊𝑐[𝑎𝑡−1,𝑥 𝑡]+𝑏 𝑐)(1) Γ𝑢=𝜎(𝑊𝑢[𝑎𝑡−1,𝑥 𝑡]+𝑏 𝑢)(2) Γ𝑓=𝜎(𝑊𝑓[𝑎𝑡−1,𝑥 𝑡]+𝑏 𝑓)(3) Γ𝑜=𝜎(𝑊𝑜[𝑎𝑡−1,𝑥 𝑡]+𝑏 𝑜)(4) 𝑐𝑡=Γ 𝑢∗𝑐𝑡+Γ 𝑓∗ 𝑐𝑡−1 (5) 𝑎𝑡=Γ 𝑜∗ tanh (𝑐𝑡)(6) where Wu,Wf,Wo,bu,bf,andboare the weights and the bias that govern the behavior of the Γu,Γfand Γogates, respectively, whereas Wcand bcare the weights and bias of the ctmemory cell candidate. An illustration of a hidden unit in aN LSTM deep learning model is shown in Figure 3. 4.2 CVOA The CVOA is a bioinspired metaheuristic first proposed by Martínez-Álvarez et al. (2020). CVOA was developed based on the COVID-19 spreading model, the disease caused by the SARS-CoV-2 virus, first reported in 2019. One of the main features lies in its remarkable trade-off between intensification and diversification to efficiently explore the search space. In this work, the CVOA is employed to optimize the hyperparameters of an LSTM model, but the authors claimed that it can be used to optimize any kind of algorithm. The LSTM hybridization was done through a new dynamic individual codification proposal. Every individual can be of different lengths, according to the number of layers the individual codifies. Furthermore, real data from the Spanish electricity market were used to assess its performance, reaching quite remarkable results in terms of accuracy and outperforming other well-established models optimized with other metaheuristics. CVOA mimics how the coronavirus infects and spreads the disease. In particular, every infected individual identifies one solution, and the infection process stands for the exploration of new solutions. As for any metaheuristic, CVOA must ensure both intensification and diversification. On the one hand, the intensification is controlled as follows. It is well-known that the infection rate for COVID19 is 3 when no face masks are worn, social distancing Tis not followed, or no vaccines had been inoculated into the population (WHO, 2021), which means that every infected individual can infect three more individuals on average. In other words, given a solution (infected individual), three new solutions are explored (three new individuals are infected from the current one). Additionally, the existence of super-spreaders has also been reported in the literature. This involves a high infection rate for such individuals; that is, certain infected individuals will infect more than three individuals, on average. On the other hand, the diversification is controlled by considering that some individuals can travel and visit regions of the search space that are far away. In other words, travelers will lead to the exploration of new solutions quite dissimilar. It is worth mentioning that all probabilities and rates have been retrieved from the real values of the COVID19. This prevents the user from consuming time in adjusting the CVOA parameters because all of them are set by default. However, different values can be assigned to BUI ET AL. 7 FIGURE 3 Description of the hidden unit in a long short-term memory (LSTM), *and +operators identify the multiplication and sum of the element-wise vector, respectively simulate different strains, with higher fatality rates or higher infection rates, for instance. A very useful feature is the parallel implementation, also proposed in this work, since it explains how to run different strains with different setup values. The main CVOA steps can be summarized as follows: 1. Step 1: Patient-zero (PZ) generation. This step consists of randomly generating the initial solution. If previous knowledge about the problem is known, this step can be avoided and the optimization process cane be started from any arbitrary solution. 2. Step 2: Spreading the disease. Every solution will infect new ones, according to some parameters such as the probability of death (solutions that will not be explored), spreading rate (the number of new solutions explored from a previous one), super-spreading rate (same as the spreading rate but with higher values), traveling probability (infection of quite dissimilar solutions for a better exploration of the search space). 3. Step 3: Updating populations. CVOA maintains three different sets of solutions: infected (current iteration), deaths (solutions that cannot infect anymore), and recovered (solutions already explored that might reinfect if the re-infection probability is met). 4. Step 4: Stop criterion. CVOA ends its execution after a given number of iterations or if the infected population is empty. 5PROPOSED HYBRID APPROACH FOR DEFORMATION FORECASTING OF HYDROPOWER DAMS This section describes the dataset (Section 5.1)anddiscusses the configuration for the CVOA-LSTM (Section 5.2). 5.1 Dataset description As mentioned above, in this work, we employed the measured data at the PV6 point (see Figure 1)fornearly22 years, from January 23, 1998, to September 5, 2019, with 260 measured cycles, retrieved on a monthly basis. Since machine learning models are based on time-series measured data only, without considering the physical characteristics of the dam materials in the modeling (Salazar et al., 2016), therefore, to forecast the dam deformation, it is necessary to determine its influencing factors. Literature review shows that hydraulic load, temperature, and dam age (Bui et al., 2018; Dai et al., 2018;Kang et al., 2017; Lin et al., 2019; Luo et al., 2019; Ren et al., 2020; Shi et al., 2018; Zou et al., 2018) are the main influencing factors; therefore, in this research, UpL, UpL, t,andθwere considered. Because the dam deformation modeling in this research uses the concept the HST that is widely accepted and used by engineers in the dam modeling (Salazar et al., 2015), therefore, higher orders of UpL should be considered, that is, UpL2, UpL3, UpL4, whereas time lags of tcanbeused as t15,t30,t45,andt60, which are the air temperature at 15, 30, 45, and 60 days, respectively, before each measuring cycle. Regarding the dam age, both θand ln(θ)shouldbeused (Stojanovic et al., 2013). As a result, 12 input factors used are UpL, UpL2, UpL3, UpL4, DoL, t,t15,t30,t45,t60,θ,ln(θ), whereas the output is the HD value. In order to avoid a potential bias deformation modeling of the dam, all input values were normalized in a range from 0 to 1 (Bui et al., 2018). Training the model is a key step in time-series forecasting. The use of k-fold cross-validation is not considered in this work due to some well-known limitations in timeseries forecasting: use of future values to predict past ones, 8BUI ET AL. the existence of gaps in time leading to the loss of relevant information, and data leakage in training and test. However, the time-series data were separated into two subsets, with a 70/30 ratio. The first subset is that the training dataset has 160 cycles, measured from January 23, 1998, to February 17, 2011 (with, again, a 70/30 ratio for training and validation), whereas the second subset is the test set consisting of 100 measured cycles from March 14, 2011, to September 5, 2019. Other similar strategies such as time-series split and block time-series split () could have been used, but preliminary results generated worse results, probably due to the small size of the dataset. Besides, it was expected that data de-trending and scaling may have improved the results, but, unfortunately, such preliminary experimentation led to worse results in terms of accuracy and all performance metrics considered in this work. 5.2 Configuring the CVOA-LSTM model For establishing the LSTM model for forecasting the deformation of the hydropower dam, it is necessary to properly determine three parameters: number of layers (L), learning rate (LR), and dropout (Drop), because they strongly influence the forecasting capability of the resulting model. The literature review showed that no thump rule is available for the determination of these parameters; therefore, in this work, the CVOA is proposed to search and optimize the three elements: 1. Number of hidden layers (L): This element identifies the possible number of layers in the architecture of the LSTM. In this work, a restriction to 1 <L≤11 was considered. 2. Learning rate (LR): This variable encodes the learning rate used in the LSTM. In this research, we considered values as 100,10 –1,10 –2,10 –3,10 –4,and10 –5. 3. Dropout (Drop): This parameter encodes the LSTM dropout in the interval [0, 0.45], with step 0.05. Herein, a three-dimensional searching space (L, LR, and Drop) is established. L is of the utmost relevance and is highly related to the variable length of the individual because, for every layer, the number of neurons must be encoded. For instance, if L =4, then four new values would be optimized, corresponding to the number of neurons existing in each of these four layers. The number of possible neurons per layer is in the range [25, 300], with step 25. An illustration of the individual codification proposed to hybridize the CVOA-LSTM model is depicted in Figure 4. The parameters adopted for the CVOA in this analysis are depicted in Table 2. It is worth mentioning that one of the main features of CVOA is that such configuration is suggested to be always the same (Martínez-Álvarez et al., 2020) since CVOA mimics the COVID-19 spreading model, and the metrics and statistics are well-known. It is also true that these metrics have evolved over time as the pandemic has shown new statistics across the world. But it has been decided to use the original parameter values proposed since the use of some others may deeply vary the functioning of CVOA, which is not the scope of this paper. 6 RESULTS AND ANALYSIS Please note that, in this project, the time-series data were processed and visualized using Microsoft Excel 2020 and ArcGIS Pro 2.6. The code of the proposed hybrid model is available at Martínez-Álvarez et al. (2020), whereas the benchmark algorithms above are available at WEKA 3.7.10. 6.1 Objective function and performance assessment of the CVOA-LSTM model In order to measure if the combination of the three parameters (L, LR, and Drop) is the best or not, a cost function must be employed. In this research, mean absolute error (MAE) in Equation (7) was employed as the cost function: MAE = 1 𝑛 𝑛 ∑ 𝑖=1 |||𝑑𝑖−ˆ 𝑑𝑖|||(7) The selection of this metric lies in the need of discovering absolute values for the dam displacements. While other problems are likely to express the errors in relative terms and use metrics such as mean absolute percentage error, in this study, this value does not provide relevant information. Besides, the quality of the resulting model was further assessed and quantified using the popular statistical metrics in the field of HD, such as root mean square error (RMSE) and coefficient of determination (R2;M.Lietal., 2019; Salazar et al., 2017;Suetal.,2018), as shown below: RMSE = √ √ √ √1 𝑛 𝑛 ∑ 𝑖=1 (𝑑𝑖−ˆ 𝑑𝑖)2(8) 𝑅2=1−∑𝑛 𝑖=1 (𝑑𝑖−ˆ 𝑑𝑖)2 ∑𝑛 𝑖=1 (𝑑𝑖− 𝑑𝑖)2(9) BUI ET AL. 9 FIGURE 4 Proposed codification for the individual in this research TABLE 2 The employed parameters for the coronavirus optimization algorithm (CVOA) algorithm No Parameter Description Value 1 Prob. D Probability of dying 0.05 2 Prob. SS Probability of being a super-spreader 0.10 3 Prob. RI. Probability of reinfection 0.02 4Prob. IS. Probability for an individual of being isolated 0.70 5 Prob. TV Probability of traveling to other search space regions 0.10 6Social Dist. Number of iterations without social distancing [7, 12] 7 Pan. DR. Number iterations 20 8Strains Number of threads 4 9 Np Number of coronavirus in the population 30 6.2 Training and validating results of the CVOA-LSTM model The training process for the CVOA-LSTM was started by randomly generating an initial individual and named as PZ. Herein, the position of PZ with three coordinates (L, LR, and Drop) in the three-dimensional searching space is a solution for the CVOA-LSTM, and the quality of the solution is measured by MAE. The training process was continued where the spreading the disease phase was activated, and 30 individuals were affected. Then, every individual infects new ones, and a new population was updated. With the new population, the MAE value for each CVOA-LSTM model corresponding to each individual was computed and compared to find the optimized one. This was an iteration process. The proposed CVOA-LSTM approach has obtained very competitive results, with RMSE =0.26 cm, MAE =0.23 cm, and R2=0.912, which were reached after the ninth iteration and just some improvements were reported during the next five iterations. Then, no improvement was derived. For this reason, the stop criterion was met, and the execution was stopped after only 12 iterations. Table 3shows the metrics evolve after each iteration. We see that the best results are derived with the individual [4, 3, 2] +[3, 3], which were decoded to the following values: the learning rate is 10–4, the dropout is 0.2, and the number of the hidden layers is 2, whereas the number of neurons for each layer is 100. After the 12 training iterations, RMSE and MAE of the CVOA-LSTM model are 0.24 and 0.21 cm, respectively, which are significantly lower than the standard deviation value of the HD (2.20 cm, Table 1). These indicate that the CVOA-LSTM model performed well. 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Deformation forecasting of a hydropower dam by hybridizing a long short-term memory deep learning network with the coronavirus optimization algorithm. Comput Aided Civ Inf. 2021;1–19. https://doi.org/10.1111/mice.12810 APPENDIX This appendix is included to show visual information for the methods used to assess the performance of CVOALSTM. BUI ET AL. 17 FIGURE A1 R2of the HD models on the validation dataset: (a) the sequential minimal optimization for support vector regression (SMO-SVM) model, (b) the Gaussian process (GP) model, (c) the M5 model tree (M5’) model, and (d) the MLPNeuralNet model FIGURE A2 R2of the HD models on the test dataset: (a) the SMO-SVM model, (b) the GP model, (c) the M5’ model, and (d) the MLPNeuralNets model 18 BUI ET AL. FIGURE A3 Predicted HD values versus measured HD values and the residual of the SMO-SVM model (a,b) and the GP model (c,d). The M5’ (e,f) and the MLPNeuralNets model (g,h) BUI ET AL. 19 FIGURE A3 Continued View publication statsView publication stats