An Automated Framework for the Health Monitoring of Dams Using Deep Learning Algorithms and Numerical Methods

Abstract

Aiming to investigate the problem that dam-monitoring data are difficult to analyze in a timely and accurate automated manner, in this paper, we propose an automated framework for dam health monitoring based on data microservices. The framework consists of structural components, monitoring sensors, and a digital virtual model, which is a hybrid of a finite element (FE) model, a geometric model, a mathematical model, and a deep learning algorithm. Long short-term memory (LSTM) was employed to accurately fit and predict the monitoring data, while dynamic inversion and simulation were used to calibrate and update the data in the hybrid model. The automated tool enables systematic maintenance and management, minimizing errors that are commonly associated with manual visual inspections of structures. The effectiveness of the framework was successfully validated in the safety monitoring and management of a practical dam project, in which the hybrid model improved the prediction accuracy of monitored data, with a maximum absolute error of 0.35 mm. The proposed method can be considered user-friendly and cost-effective, which improves the operational and maintenance efficiency of the project with practical significance.

1. Introduction

Dams have played a pivotal role in national life over the past few decades because they have secured water supply, reduced flood hazards, and maintained healthy and stable social development [1]. However, dam materials can degrade over time, and dam structures can experience a sudden increased load, both of which can lead to catastrophic failure [2]. Dam safety monitoring (DSM) is recognized as a valuable method for detecting critical responses to structures, with the aim of providing warning of anomalies or accidents at an early stage [3,4].

With the evolution of sensing and automation technology [5], it is now possible to easily collect massive amounts of high-quality data. However, after several years of operation, the amount of information in the raw and preprocessed data (data, images, etc.) can reach hundreds of gigabytes, which can lead to data mismatches and quite time-consuming access [6]. In addition, the advantages of hybrid models combining structural simulation and statistics continue to emerge [7,8,9,10,11]. However, it has become a great challenge to design and implement an automated framework that includes data storage, transmission, visualization, manipulation, and analysis.

This paper highlights and implements an automated monitoring framework. The initial step is the introduction of the PAD algorithm to detect and generate an alarm regarding the outliers in the monitoring data to provide reliable data for the dynamic inversion and the LSTM model. A hybrid model consisting of dynamic inversion and the LSTM algorithm is proposed to improve monitoring. When the monitored value of the water level fluctuates frequently, the material parameters are obtained via dynamic inversion, and then the FE simulation of the mesh is performed to correct the predicted values of the LSTM. Data acquisition, hybrid model analysis, visualization, and anomaly alarm are integrated to establish the automated monitoring framework. Finally, the proposed framework is validated with an example of safety monitoring on an engineering project, confirming that the FE simulation corrects the data to an accuracy of 95%. The application shows that the system improves the efficiency of operation and enables engineers to have a real-time, clear, and accurate picture of the dam’s operational status.

2. Related Work

Monitoring models can be classified into statistical models, deterministic models, hybrid models, and intelligent algorithm models [4]. Statistical models that define the mapping between influences and measured influences as multivariate linear or multivariate nonlinear offer the benefits of computational efficiency and simplicity. Lew et al. excluded the effect of aging on dam deformation and proposed a hybrid model that integrated linear and nonlinear factors to minimize the residual [12]. Wang et al. proposed a hydraulic, hysteresis, seasonal, and temporal (HHST) model for the deformation of extra-high concrete dams [13].

However, the mechanisms of dams cannot be clearly explained using these models in terms of the evolution process, and the prediction accuracy is greatly degraded in the case of fewer monitoring data or more noise factors [14,15]. Although deterministic models can clearly capture the behaviors of dam structures, it is difficult to promote these models in practical engineering due to the large number of simulation calculations [16]. Intelligent algorithmic models are characterized by high computational efficiency and the strong fitting ability of nonlinear mapping [17,18]. Lin et al. proposed a novel dam health monitoring model using optimized sparse Bayesian learning and sensitivity analysis, mainly for monitoring radial displacement and seepage [19]. Cheng et al. compared the results of support vector machines, artificial neural networks, and hybrid artificial intelligence models in dam displacement prediction [20]. Kang et al. compared the outputs of the GPR-HST model with the GPR model and concluded that the GPR approach is more effective in capturing the nonlinearity of the dam response [21]. Chen et al. proposed a novel method for predicting the displacement probability of concrete dams based on the optimized relevance vector machine (ORVM) [22].

However, intelligent models have high parameter sensitivity and are prone to overfitting [18]. The hybrid model combines structural simulation and statistics, which can better explain the mechanism of structural changes in dams, simplify the analysis difficulty, and is widely used in practical engineering. Karimi et al. combined artificial neural networks (ANNs) and the finite element–boundary element (FE-BE) model to predict the features of concrete gravity dams [7]. Lin et al. proposed a model to separate the deformation of the dam body displacement from the dam foundation constraint displacement, in which the collected monitoring data were used to calibrate the zonal model [8]. Wei et al. introduced a spatial–temporal hybrid model by considering the chaotic effect of the residual series to monitor the deformation of concrete arch dams [9]. Shao et al. proposed a random coefficient model based on panel data, which solves the problem of multicollinearity of traditional regression methods by using time series and cross-sectional data [10]. Lin et al. proposed a novel inversion framework that uses a surrogate model instead of the finite element model in the optimization loop [11].

The work of the above-mentioned scholars explores or improves one aspect of monitoring. As the service life of a structure increases, more and more costs need to be invested. Improvements in automation and reduced consumption have garnered the attention of scholars. A comprehensive scaling method of bridge structural deformation detection using multitemporal satellite-based differential interferometry is presented to automatically interpret the deformation of a specific bridge and prioritize the level of monitoring/assessment [23]. Zhu et al. implemented an online visualization system using WebGL to load and render models, but there are some limitations in terms of free user interaction, which affects the visualization effect to some extent [24]. An expert system model covering anomaly importation and safety monitoring is proposed, which allows for the real-time monitoring of dam safety throughout the process [4].

In the existing work described above, there is a lack of an automated framework that processes continuous data using a microservice framework to analyze and correct data, and predict structural data values in real time. Therefore, our work focuses on the design and implementation of a framework for such real-time DSM applications.

3. An Automated Framework for DSM

An integrated online, real-time, and automated monitoring framework is established with four major components, namely data acquisition, hybrid model monitoring, outliers warning, and visualization, as shown in Figure 1.

3.1. Data Preprocessing

3.1.1. Collection

There are two types of data collection: automatic and manual. Automatic acquisition is the process of converting the physical quantities collected with sensors into electrical signals, sending them to the host computer, and then transferring them via TCP to the data-receiving module, where they are stored and analyzed. For structured data, the data-parsing process is not the same for different collectors, as different collectors correspond to different hosts, which have different data formats. The collector calls the corresponding data-parsing interface to obtain the collector number, the collection time, the measured value, and other information.

The data collected during a manual inspection are manually entered into the datasheet with sensor numbers. The field data and project inspection photos are sent to the database via the GPRS network for further application. The automatic collection and manual collection of monitoring data are linked to the database by setting the collection type of the database table in accordance with different storage methods.

3.1.2. Storage

The storage of data is very important. A well-designed data relationship table is significant for the platform, as all the visualization and analysis functions are based on the database.

First, the geometric model data for monitoring sensors and dam sections include information such as name, global ID, geometric parameters, material, spatial location, etc. These data are parsed using visualization techniques and then stored in the database. Second, the storage of monitoring data mainly involves the basic information of monitoring equipment, calculation parameters, monitoring type, monitoring time, status, manufacturer, etc. Then, the monitoring data including deformation, water level, temperature, water pressure, stress, and strain values are stored. Finally, the relevant data from the calculations are stored, including the time of the calculation, the point number, the calculated value, and the threshold values for the various instruments. The data are stored in different tables, and each table is associated with others using keywords. The keyword design and description of some tables are shown in

Table 1. Data tables and keywords.

Name	Keywords
MEASPOINT	ID, DCODE, TYPEID, BUILDINGID, DTYPE, RUNSTATE, V1UP, V1UUP, V1DOWN, V1UDOWN, R1UP, R1UUP, R1DOWN, R1UDOWN,
SENSORTYPE	ID, MCID, V1NAME, V1UNIT, R1NAME, R1UNIT
MONITORCLASS	ID, NAME
DATAMEAS	ID, POINTID, DT, V1, R1, EVV1, EVID1, ISVERIFIED

.

3.1.3. Integration

The integration of data is the organic formation of links between different types of data such as monitoring data, geometric data, and spatial information, extending the dimensionality of the data. This allows the original static geometric model to be extended to a dynamic model overlaid with monitoring data, which extends the presentation of monitoring data into three dimensions, making it clearer and more realistic, greatly improving visualization, and enhancing easy management.

The first step involves parsing the model generated using Building Information Modeling (BIM) and decomposing the overall model into several submodels (dam sections, monitoring instruments, etc.), which are the basis for integrating the monitoring data with the model. Managers can access all the data of a submodel by indexing them in the BIM model based on the identifier, which is unique. The model information is stored in an object (‘uuid’: ‘2B90C7C4-572C-4263-8966-E48367E6C5D3′,’name’: ‘TC2′, …). In the data, the most important feature is the ID and sensor number of the submodel, so the parsing process mainly involves the extraction of the ‘uuid’ and ‘name’ attribute values of the object. However, with many monitoring sensors, automatically mapping the instruments to the submodels is crucial. Thus, the sensor number is assigned to the submodel during the creation of the model to achieve the association. There are two keywords in the table—‘ELEMENTID’ and ‘DCODE’. The first keyword refers to the number of the sensor model in the whole model, and the second keyword is associated with the ‘DCODE’ of the sensor information table. The tables in the database are related to each other by keywords to form a linked whole between the tables, as shown in Figure 2.

3.2. Mechanism Model of Dam

For structures with complex structural forms and many degrees of freedom, the finite element method (FEM) is the best choice, which is currently the most popular calculation method in academia and industry for modeling structural distribution patterns from temperature to seepage, stress, and displacement [14,25].

3.2.1. Mechanical Model

The elastic modulus of the overall finite element model containing the dam body and dam foundation is denoted as $(E_i,i=1,n)$, where $n$ is the number of material zones. The mechanical formulation of the model can be expressed as follows:

$$\left\{\begin{array}{l}Ku=F, \mathrm{on} \Omega \\ u=\overline{u}, \mathrm{on} \Gamma \end{array}\right.$$

(1)

where $\Gamma$ is the displacement boundary, $\Omega$ is the problem domain, $K$ is the overall stiffness matrix, $u$ is the displacement array to be solved, $F$ is the node load array, and $\overline{u}$ is the known displacement boundary constraint. The problem can be decomposed into $n$ subproblems based on the number $n$ of model partitions:

$$\left\{\begin{array}{l}{K}^i{u}^i=F^i, \mathrm{on} {\Omega }_i\\ u^i={\overline{u}}^i, \mathrm{on} {\Gamma }_i\\ u^i=u^j, \mathrm{on} {\Gamma }_{ij}={\Omega }_i\cap {\Omega }_j\\ i\ne j \mathrm{and} i,j=1,\cdots ,n\end{array}\right.$$

(2)

The stiffness matrix $K^i$ in the equilibrium statement of the above equation is a symmetric singular matrix, which cannot be solved for the displacement directly. It is transformed into the following shape:

$$\left[\begin{array}{c}{K}_{dd}^i\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{K}_{dc}^i\\ K_{cd}^i\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{K}_{cc}^i\end{array}\right]\left[\begin{array}{c}{u}_d^i\\ u_c^i\end{array}\right]=\left[\begin{array}{c}{F}_d^i\\ F_c^i\end{array}\right],u_c^i={\left.u^i\right|}_{{\Gamma }_i\cup {\Gamma }_{ij}}$$

(3)

where $u_d$ and $u_c$ are the displacements to be solved and the given displacements; and $K_{dd}$, $K_{dc}$, $K_{cd}$, $K_{cc}$, $F_d$, and $F_c$ are the corresponding stiffness matrices and the block matrices of the load vectors. Let $F_{*}^i=F_{\mathrm{d}}^i-K_{\mathrm{d}\mathrm{c}}^i{u}_{\mathrm{c}}^i$; the above equation can be expressed as (4):

$${K_{\mathrm{d}\mathrm{d}}^i{u}_{\mathrm{d}}^i=F_{*}^i,K}_F{u}_d=F_{\ast }$$

(4)

According to the rule of block symmetric matrices, it can be obtained as follows:

$$u_{\mathrm{d}}=K_F^{-1}{F}_{\ast }=\sum _{i=1}^n \left(\frac{I{K}_F^i}{E_i}\right)F_{\ast }=\sum _{i=1}^n \frac{1}{E_i}\left(I{K}_F^i{F}_{\ast }\right)$$

(5)

3.2.2. Dynamic Inversion Analysis Model

However, the structure is subjected to various forms of loading involving permanent loads, the self-weight of the structure, hydraulic load, seepage load, and temperature load from changes in ambient temperature. Vehicle loads are also considered when the top surface of the dam allows for vehicle traffic. The material parameters of the various parts of the structure have changed considerably from their design values over the years of operation. Moreover, time-invariant parameters are mostly stochastic rather than invariant, so the results obtained with traditional statistical methods usually have large variability.

The cuckoo search (CS) is widely used in complex optimization problems in scientific research and engineering because of its advantages of self-organization, good parallelism, strong global search capability, and easy integration with other algorithms [26]. The CS is a global optimization algorithm based on cuckoo breeding strategy and Levy flight behavior: (1) First, a set of individual cuckoos (also known as nests) is initialized at random, with each nest representing a potential solution. (2) The fitness of the problem is computed. (3) The birds’ nesters with the higher fitness are selected as the current optimum. (4) A new bird’s nest is randomly generated to replace the current worst bird’s nest, or the current optimal solution is transformed to generate a new bird’s nest to replace the current worst bird’s nest. (5) The algorithm stops if the stopping condition is met (e.g., the maximum number of iterations is reached, or the fitness meets a given value); otherwise, the process returns to step 2.

Therefore, the CS was applied to inverse the mechanical parameters of the dam in order to obtain property values that correspond to the current state of the structural materials. The calculation steps are shown in Figure 3. The elastic modulus of the material in the .mat file was automatically modified to the latest value using Python programming language with every finite element simulation. The table was constructed in a database to store the results of the back analysis. When monitoring data were updated, the results of the previous inversion were set as material parameters, and a forward analysis was performed to evaluate the monitoring data. Boundary conditions in the simulation were based on the measured data, including water level, water temperature, and air temperature. Depending on the evaluation results, it was determined whether further back analysis would be required.

3.3. Data-Driven Model

The LSTM is a recurrent neural network model whose cells are structured as presented in Figure 4 [27]. The update of the cell state is controlled by forgetting gates, input gates, and output gates. The data in the cell state are decided to be dropped or added at the forgetting gate and input gate, respectively, while the output gate decides the output of the cell state. The LSTM is more suitable for predicting the deformation of dams because of its advantage of being able to effectively use time series data over long distances [27,28,29]. The historically monitored data are assumed to be $D^S=\left\{x_1^S,x_2^S,\cdots x_t^S\right\}$. From Equations (6)–(8), it can be seen that the parameters are calculated during the forward propagation of the model.

The LSTM model is computed in three main stages:

The forgetting stage mainly involves the forgetting gate $F_t$, which determines the information that should be discarded or retained from the previous state. $F_t$ activates the $\sigma$ function based on the output $h_{t-1}$ of the previous moment and the current memory cell input $C_t$, and outputs the result, which is multiplied by the memory cell state $C_{t-1}$ of the previous moment to produce a number between 0 and 1, where 0 indicates the complete discarding of the previous state information and l indicates the complete retention of the previous state information, calculated using the following formula:

$$F_t=\sigma \left(W_{fh}·h_{t-1}+W_{fx}·x_t+b_f\right)$$

(6)

In the selection-memory phase, the input gate $I_t$ decides whether to update the current information into $C_t$, and ${\tilde{C}}_t$ generates the output $h_t$ of the next state’s implicit layer based on $h_{t-1}$, $C_t$, and $tanh$, which is calculated as follows:

$$\begin{array}{c}{I}_t=\sigma \left(W_{ih}\cdot h_{t-1}+W_{ix}·x_t+b_i\right)\\ {\tilde{C}}_t=tanh\left(W_{ch}\cdot h_{t-1}+W_{cx}·x_t+b_c\right)\\ C_t=F_t⨀C_{t-1}+{\tilde{C}}_t⨀I_t\end{array}$$

(7)

In the output stage, the result of the input gate is multiplied by the $\sigma$ function to identify what information needs to be output from the memory cell. The result of the output gate $O_t$ is multiplied with the activation function tanh to obtain the final output $h_t$, which is calculated as follows:

$$\begin{array}{c}{O}_t=\sigma \left(W_{oh}\cdot h_{t-1}+W_{ox}·x_t+b_o\right)\\ h_t=O_t⨀tanh\left(C_t\right)\end{array}$$

(8)

where $x_t$ is the input series at time $t$; $W_{fx}$, $W_{ix}$, $W_{cx}$, and $W_{ox}$ are the weight matrices acting on the current input sequence; $W_{fh}$, $W_{ih}$, $W_{ch}$, and $W_{oh}$ are the weight matrices acting on the last output sequence; $b_f$, $b_i$, $b_c$, and $b_o$ are the corresponding bias vectors; ${\tilde{C}}_t$ is the cell candidate vector of time $t$; and $⨀$ is the Hadamard product.

3.4. Hybrid Model for DSM

The variation in the material properties of the dam can be well reflected using the mechanistic model, as it can reduce the effect of noise. However, it is difficult to respond to external environmental changes on time. The data-driven model is capable of dynamic learning and self-optimization based on current data and is highly time-sensitive and accurate. However, it cannot predict data for the parts of the dam where sensors are not installed. Also, the data model is susceptible to noise, which is frequently collected during the operation of the sensors.

A combination of the mechanism model and the data-driven model was used to build a more accurate model in order to achieve the complementary strengths of both. The process of creating the hybrid model is shown in Figure 5. First, the material parameters were obtained using dynamic inversion. In the second step, the water level with a rate of change higher than the threshold was applied as a load and boundary constraint to the calculation. Next, the monitored data in the selected date were preprocessed and then divided into training and test sets to be input into LSTM for fitting and prediction. Finally, the simulated value was used to replace the predicted data where the rate of change in the water level exceeded the threshold to generate the complete time series. $p_l$, $p_m$, and $m_e$ represent the predicted values of the data-driven model, the predicted values of the mechanistic model, and the monitored data of environmental variables, respectively; $p_{l,t}$, $p_{m,t}$, and $m_{e,t}$ are the monitored values at time $t (1\le t\le n)$; ${\delta }_l$ is the threshold value of the data variation rate; and $d_p$ is the predicted value of the hybrid model, which is a combination of the simulated and predicted values.

3.5. Outlier Detection and Warning

The basic characteristic of an outlier is the presence of an isolated value significantly larger or smaller than $t_{i-1}$ and $t_{i+1}$ at $t_i$. Persist anomaly detection (PAD) compares the value at $t_i$ with the value in the previous time window and identifies the value as an outlier if it varies from the mean or median in the window to an unusually large degree. The key training parameters of the algorithm are the number of previous time series values contained in the time window ($w$) and the coefficient ($c$) used to determine the normal range boundaries based on the historical interquartile range. Three metrics, namely precision, recall, and $F1$ score, are used to evaluate the outlier detection performance of the method. The greater the precision, recall, and $F1$ score, the more accurate the PAD. The three metrics are calculated as follows:

$$Precision=TP/\left(TP+FP\right);Recall=TP/(TP+FN)$$

(9)

$$F1=2\times recision\times Recall/(Precision+Recall)$$

(10)

where $TP$ is the number of outliers correctly detected, and $FP$ is the number of data incorrectly identified as outliers. $FN$ is the number of outliers incorrectly identified as valid data.

When the monitoring data are stored in the database, the proposed framework automatically calls the PAD algorithm to detect the value of each sensor, marks the sensor corresponding to the outlier in a red eye-catching font, and displays the information of the instrument such as the dam section and elevation, the measured value, and time. At the same time, the abnormal information is discarded and an alarm is generated to remind the managers of different departments and permissions to achieve the real-time sharing of warning information.

4. Engineering Application

In this paper, the proposed approach is demonstrated using a concrete gravity dam. The developed model in Revit is integrated with the monitoring data from the DSM platform. All results are displayed with a browser web page as the visualization platform in order to make it easier for engineers to manage the application.

4.1. Details of the Dam and Sensors

The development of the platform needs to be based on practical application requirements. The proposed platform is for a high concrete gravity dam with a foundation elevation of 41 m and a maximum height of 112 m, as illustrated by the physical structure in Figure 6. The dam was constructed in September 2007 and completed in December 2011 for power generation. A total of three foundation reinforcements were subsequently carried out (the last in August 2014). The layout of the sensors is shown in Figure 7.

4.2. The Hybrid Model Verification

4.2.1. Factor Selection for the LSTM Model

When using the LSTM as a dam displacement prediction method, the input factors consider three main factors and residual, as shown in (11). The output is the displacement measured with sensors.

$$\delta ={\delta }_H\left(t\right)+{\delta }_T\left(t\right)+{\delta }_{\theta }\left(t\right)+\epsilon$$

(11)

where $\delta$ represents the predicted displacement of the dam, ${\delta }_H\left(t\right)$ represents the hydraulic component, ${\delta }_T\left(t\right)$ represents the thermal component, ${\delta }_{\theta }\left(t\right)$ means the aging component, and $\epsilon$ is the residual.

The hydraulic component of a gravity dam can be depicted using a cubic polynomial function of the reservoir water level as $X_1=H-H_0,X_2=H^2-H_0^2$, and $X_3=H^3-H_0^3$, where $H_0$ denotes the data on the initial monitoring day, and $H$ denotes the data on the current monitoring day.

When the temperature monitoring period is not continuous, or the measured value is not available, the thermal component can be expressed with a combination of harmonic functions. In this paper, multiperiodic harmonic factors are chosen to represent the thermal component:

$$\begin{gathered} X_4=\mathit{sin}\frac{\pi t}{365}-\mathit{sin}\frac{\pi t_0}{365},X_5=\mathit{cos}\frac{\pi t}{365}-\mathit{cos}\frac{\pi t_0}{365}, \\ {X}_6=\mathit{sin}\frac{2\pi t}{365}-\mathit{sin}\frac{2\pi t_0}{365},X_7=cos\frac{2\pi t}{365}-cos\frac{2\pi t_0}{365} \end{gathered}$$

(12)

where $t_0$ and $t$ are the same as $H_0$ and $H$, respectively.

The irreversible component reflects the plastic deformation of the dam in a certain direction with time. It can be approximated with a polynomial function containing four types of functions. The four factors chosen are as follows:

$$X_8=\theta -{\theta }_0,X_9=ln\theta -ln{\theta }_0,X_{10}=\frac{\theta -{\theta }_0}{\theta -{\theta }_0+1},X_{11}=1-e^{-\left(\theta -{\theta }_0\right)}$$

(13)

where ${\theta }_0$ is $t_0$/100, and $\theta$ is t/100.

In summary, the statistical model for the horizontal displacement of the dam is shown in (14).

$$\begin{array}{r}\delta =a_0+{\displaystyle \sum _{i=1}} a_i\left(H^i-H_0^i\right)+{\displaystyle \sum _{i=1}^2} \left[b_{1i}\left(\sin \frac{\pi it}{365}-\sin \frac{\pi i{t}_0}{365}\right)+\right.\left.b_{2i}\left(\cos \frac{\pi it}{365}-\cos \frac{\pi i{t}_0}{365}\right)\right]\\ +c_1\left(\theta -{\theta }_0\right)+c_2\left(\mathrm{l}\mathrm{n}\theta -\mathrm{l}\mathrm{n}{\theta }_0\right)+c_3\frac{\theta -{\theta }_0}{\theta -{\theta }_0+1}+c_4(1-e^{-\left(\theta -{\theta }_0\right)})\end{array}$$

(14)

4.2.2. Evaluation Indicators and Training Settings

This paper illustrates the proposed system tool with displacement monitoring data collected from 25 December 2019. The sensors were monitored at a frequency of 1 day, thus providing seven monitored values per week. The series of monitored values were divided into two subsets. The first subset comprised 70% of the data, with a total of 748, and was used to train the model. The second subset comprised 30% of the data and was applied to validate the model. For the setup of the model training process, the root-mean-squared error ($RMSE$), mean-squared error ($MAE$), maximum absolute error ($MAXE$), and coefficient of determination ($R^2$) were used as training metrics, with the following equations:

$$RMSE=\sqrt{{\sum }_{i=1}^n{(y_{f,i}-y_{m,i})}^2/n}$$

(15)

$$MAE=\frac{1}{n}\sum _{i=1}^n \left|y_{f,i}-y_{m,i}\right|$$

(16)

$$MAXE=max\left|y_{f,i}-y_{m,i}\right|$$

(17)

$$R^2=\frac{{\left[\sum _{i=1}^n \left(y_{f,i}-\overline{y_f}\right)\left(y_{m,i}-\overline{y_m}\right)\right]}^2}{\sum _{i=1}^n {\left(y_{f,i}-\overline{y_f}\right)}^2\sum _{i=1}^n {\left(y_{m,i}-\overline{y_m}\right)}^2}$$

(18)

where $n$ is the number of datasets fitted, $y_{f,i}$ is the fitted value at step $i$, $y_{m,i}$ is the measured value at step $i$, and $\overline{y_f}$ and $\overline{y_m}$ are the mean of the predicted and monitored values, respectively. The model was trained when the $RMSE$ between the fitted and measured values of the model was minimized. In addition, using the Adam optimizer, the batch size was set to 100. Two indicators of model completion were set, namely the maximum number of training iterations (epochs = 150) and an $RMSE$ of less than 1 × 10⁻⁵. The training was immediately terminated when the RMSE was less than 1 × 10⁻⁵, or the maximum number of iterations was reached.

4.2.3. Inversion of Mechanical Parameters

First, an FE model was constructed using HYPERMESH (version 14.0) with the spatial coordinates of the model corresponding to those of the actual project, so that the node values of the model could be spatially interpolated according to the spatial position of the sensors to obtain the calculated values of the sensors. The foundation extends upstream and downstream, and the foundation depth is about two times the maximum dam height, with the X direction indicating downstream, the Y direction indicating cross-river, and the Z direction indicating vertically upward. The model was composed of hexahedral elements with a total of 5580 elements and 6234 nodes, as shown in Figure 8. Secondly, the material properties were initially defined, and the external load and constraints were set in GeHoMadrid (Version 1.0), the team’s own FE analysis software, and then discrete iterations were performed in the time and space domains to obtain the calculated values under the actual boundary conditions. A linear elastic model was used in the simulation with fixed constraints around and at the bottom of the model. According to Section 4.2.1, the hydraulic component was separated from the displacement values, and therefore only the hydraulic load was considered in the forward calculation.

In an FE simulation, multiple parameters can have an impact on the accuracy of the simulation, including density, elastic modulus, and Poisson’s ratio. Therefore, it is necessary to find the most sensitive parameter for inversion. In this paper, the elastic modulus was chosen as the parameter of inversion by combining the engineering practice and the research of other scholars [30,31,32]. Based on the material parameters of the dam body and foundation, the elastic modulus of the dam body and the foundation in the inversion were set to 20–26 $\mathrm{G}\mathrm{p}\mathrm{a}$ and 4–8 $\mathrm{G}\mathrm{p}\mathrm{a}$, respectively. The Poisson’s ratios of the dam body and foundation were set to 0.167 and 0.25, respectively. The density rates of the dam and foundation were set at 24 and 25.7 $\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$, respectively. A multisensor inversion model was used with the following objective function:

$$f=\frac{1}{mn}\sum _{i=1}^m\sum _{j=1}^n{(c_{i,j}-d_{i,j})}^2$$

(19)

where $n$ is the time step of the simulation, $c_{i,j}$ is the $i$-th sensor, with the calculated value of the $j$-th step; and $d_{i,j}$ is the $i$-th device, with the measured value of the $j$-th step.

4.2.4. Results and Discussion

(1)

Analysis of predicted results

In addition, the BP (backpropagation), GA-SVM (genetic algorithm–support vector machine), and GUASS algorithms were used to fit and predict the data and compare the results with those of the LSTM algorithm, as shown in Figure 9. The prediction accuracy for the test phase is presented in

Table 2. Error in predicted values for different algorithms.

Model	EX1-8 Testing				EX2-6 Testing
	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	$\mathit{M}\mathit{A}\mathit{E}$	$\mathit{M}\mathit{A}\mathit{X}\mathit{E}$	${\mathit{R}}^2$	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	$\mathit{M}\mathit{A}\mathit{E}$	$\mathit{M}\mathit{A}\mathit{X}\mathit{E}$	${\mathit{R}}^2$
BP	1.675	1.415	5.15	0.878	1.653	1.368	3.312	0.881
GA-SVM	1.582	1.502	4.45	0.845	1.570	1.484	2.590	0.852
GUASS	1.155	1.013	4.18	0.861	1.148	1.005	2.253	0.866
LSTM	0.476	0.353	2.71	0.906	0.458	0.347	1.327	0.932

. It is worth noting that the LSTM model has lower $RMSE$, $MAE$ and $MAXE$ and higher $R^2$ than the other models.

(2)

FE simulation and correction

As can be seen from the predicted data in Figure 9, the frequent fluctuations in the measured values lead to a decrease in the prediction accuracy, which proves that it is hard to fit the features of the data very accurately in this case. Therefore, when the monitored values fluctuated frequently, the inversion was applied to obtain material parameters, and then the predicted values were obtained using the FE simulation to improve the prediction accuracy.

When the fitness value is minimized, the output is the mechanical parameters. After obtaining the parameters, the GeHoMadrid software was used to simulate and calculate the values of the sensors. As shown in Figure 10, the simulated values were integrated with the predicted values of the LSTM. The dark red line in the red dashed box is the prediction of the simulation, while the rest of the values indicate the prediction of the LSTM. The simulated predictions are more accurate than those from the LSTM, with a $MAXE$ of 0.35 mm.

4.3. Outlier Warning

After the automated collected data are stored in the database, the proposed framework automatically calls the PAD to detect the monitored data. When anomalous data are recognized, the framework automatically discards the outlier information and, at the same time, the sensor corresponding to the outlier is displayed on the 3D model, as shown in Figure 11.

5. Conclusions

To improve dam monitoring, an automated monitoring framework is proposed in this paper. The major contributions of this study are as follows:

A hybrid model integrating the LSTM and FE simulation is proposed with the variation rate of water level as the indicator. The hybrid model had a $MAXE$ of 0.35 mm between the predicted and monitored values, which was 75% lower than the $MAXE$ of the LSTM.

An automated DSM platform is proposed and implemented by properly integrating web, microservices, databases, FE simulations, and deep learning. The proposed system can automatically monitor and warn dams in a real time and continuous manner, which reduces operation costs.

Although the back analysis is optimized, the inevitable need to call GeHoMadrid several times during the inversion process to perform the simulation reduces the operational efficiency of the system. Thus, a parallel algorithm needs to be further investigated for optimization. In addition, the threshold of the rate of change in environmental variables needs further research to clarify the balance between the predicted values and the LSTM predictions.