Research on the Digital Twin Polder Area System Driven by Integrating the Xin’anjiang Model and the N-BEATS Model

Abstract

Digital twins are propelling the next generation of the industrial revolution and serve as a key technology in enabling intelligent water conservancy. However, due to the diversity of objects within water conservancy scenarios and the complexity of related factors, research and application of digital twins in the field of water conservancy remain immature. There are still significant challenges in constructing fine-grained, high-fidelity digital twin for water conservancy objects and their corresponding scenarios. In this context, taking polder areas as research subjects, a digital twin polder area system is proposed, which includes the data representation of the main elements in the polder area; based on 3D engine Unity, the modeling and rendering of the polder area’s terrain, water body, water conservancy projects, and different weather conditions are achieved; the Xin’anjiang model, N-BEATS model, and the feature engineering model we proposed are integrated to predict water level and flow rate, thereby driving the visual scenario to simulate the extent of the impact of waterlogging at different future moments. Based on satellite imagery data, actual water level data, and flow rate data from a polder area in the Lixiahe river network of Jiangsu Province in China, we measure the efficiency of scene rendering and the accuracy of the prediction models. The results show that the performance and model accuracy of the digital twin polder area system meet the practical requirements. It is more comprehensive by comparing with other works, which can be used as a reference for the construction of a digital twin system or scenario in the water conservancy field.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Digital twin (DT) can be thought of as “a paradigm that primarily supports the exchange of information between a physical system (and its associated environment and processes) and their virtual representation for a variety of purposes” [1]. In recent years, DTs have continuously evolved and developed rapidly and have been studied and widely applied in intelligent manufacturing, smart cities, healthcare, and other fields [2–4], effectively helping the upgrading of related industries. Water conservancy is the pillar of the national economy, and it also has a huge and urgent demand for DTs [5, 6]. However, due to the complex internal mechanisms and motion patterns of many objects (rivers, water conservancy projects, polder areas, etc.) in the field of water conservancy, there are still many challenges in how to implement fine-grained, high-fidelity DTs and corresponding scenarios. To solve these problems, we take the widely distributed polder areas in the plain river network region as the research objects and propose a DT polder area system. First, the data representation of water body, water conservancy projects, weather, and other elements are depicted; then, based on Unity, a virtual scenario is constructed, implementing the modeling and rendering of the terrain, water body, water conservancy projects, and different weather conditions; on this basis, the Xin’anjiang model and N-BEATS model are integrated to predict the hydrological situation, thus enabling the virtual scenarios to vividly display the precipitation and waterlogging situations at different times.

The main contributions can be summarized as two aspects: (1) The respective data representation of water bodies, terrain, water conservancy projects, weather conditions, and other related elements is depicted, and they are stored as the universally applicable and highly shareable JSON files, providing a software-defined foundation for rapidly constructing fine-grained DT objects of the polder areas. (2) Utilizing the 3D engine Unity, a virtual polder area has been implemented; subsequently, based on the idea of combined models [7], the hydrological conditions of the polder area have been predicted by integrating the Xin’anjiang model and the N-BEATS model, thereby providing direct support for simulating the precipitation and waterlogging situations at different times in the future.

The remaining content is organized as follows. Section 2 introduces related works regarding DTs. In Section 3, the key technologies and tools are introduced. In Section 4, the architecture of the DT polder area system is proposed. Section 5 elucidates the data representation, virtual scenario construction process, and how to integrate the Xin’anjiang model and N-BEATS model for the DT polder area system. Section 6 presents a case study, followed by the experiments to validate the usability of the proposed system. The performance and functionality with related research works are also compared. At last, the whole work is summarized and some directions for future improvements are put forward in Section 7.

2. Related Work

The concept of DTs, initially posited by Grieves and Vickers in the year 2003 within his curriculum on product lifecycle management, was articulated by him as “a set of virtual information constructs that fully describes a potential or actual physical manufactured product from the microatomic level to the macrogeometrical level” [8]. Subsequently, the National Aeronautics and Space Administration (NASA) of the United States released the technical roadmap for DT [9], which was also adopted by the U.S. Department of Defense for health maintenance and support in aerospace [10]. Since then, DTs have garnered widespread attention from both the academic and industrial sectors, ushering in a period of rapid development. At present, as the novel generation of information technology for deconstructing, describing, and understanding the physical world, DT has emerged as the new focus of global information technology development. Its achievements are directly applied to various scenarios. For instance, Cimino [11] provided an overview of the development of DT technology within the manufacturing sector. Verdouw [12] proposed a conceptual framework for designing and implementing DT in farm management, applying it to smart agriculture scenarios.

The application of DT technologies facilitates the establishment of a comprehensive water resource management and allocation system, advancing the digitalization, intelligence, and precision of water resource management. It is also an important hallmark of high-quality development in water conservancy. Against this backdrop, considerable strides have been made in the integration of DT-related research and practice. Pipedream [13], an end-to-end simulation engine for real-time modeling and state estimation in natural/urban drainage networks was presented, which combined a new hydraulic solver based on the one-dimensional Saint–Venant equations and a Kalman filtering scheme that efficiently updates hydraulic states based on observed data. Though the simulation engine was effective at both interpolating hydraulic states and forecasting future states based on current measurements, the work lacked a detailed exposition of the construction process for the DT drainage network and the data representation of its components. Fuertes [14] elucidated the critical requirements for a DT water distribution system, and subsequently proposed the constructed DT water distribution system, GO2HydNet. This system integrated hydraulic modeling with multisource information from the water distribution network, whilst providing advanced analytical capabilities predicated on deep learning. Pesantez [15] devised a DT model that integrated advanced metering infrastructure data with hydraulic models to assess the impact of COVID-19-related changes in water demand on infrastructure. Bonilla [16] proposed the utilization of a graph convolutional neural network theory, associated with hydraulic models, to generate a DT implementation for water systems, effectively forecasting the states of two water supply networks. Pedersen [17] delved into the nascent concept of DTs in urban water supply systems and examined the ongoing DT implementation process at the Danish VCS company. Ranjbar [18] devised a DT system for the Canal de Garonne in northern France, which accurately depicts the dynamics of rivers and canals and can also be used to analyze past events. However, the DTs of various water network systems introduced in the above research works were mainly realized by two-dimensional visualization, lacking intuitive three-dimensional display functions and rich user interaction mechanisms, and were not yet equipped with three-dimensional calculation, forecast result simulation, and other services [19]. The authors [20] proposed a method for the reconstruction and application of DTs of inland waterway channels based on three-dimensional video fusion: By integrating drone oblique photography with BIM modeling technology, a three-dimensional scene model of the inland waterway channel was constructed, which further enables the combination of real-time discrete surveillance videos from different perspectives with the three-dimensional scene model. Barbie [21] introduced how to successfully apply the DT prototype to underwater network scenarios. However, neither of the two aforementioned studies discussed how to manage the constructed DT objects using data-driven or mechanistic models. Qiu [22] introduced a Web-based DT system that facilitates the virtual simulation of geospatial elements, integrating and coupling multiple mathematical models for the comprehensive management of the Chaohu Lake watershed. However, the study had yet to integrate the mechanism model with data-driven models, represented by deep learning, and lacks comparative analysis with related DT systems.

To sum up, DT has become the driving force behind the development of the new generation of information technology, and it currently boasts numerous research findings and applications in the field of water conservancy. However, the current DT systems tailored for the water conservancy sector lack a universally applicable solution in terms of reference architecture [23] and technology. In addition, there is a paucity of cases that integrate functions such as monitoring, forecasting, and simulation into a cohesive whole. Regarding the subject of study, to our knowledge, the research on the integration of these polder areas with DT technology remains an unexplored frontier. Therefore, a DT polder area system, propelled by integrating the Xin’anjiang model in conjunction with the N-BEATS model, has been proposed.

3. Key Technologies and Tools

Constructing a DT object with fine-grained and high-fidelity involves numerous related technologies [24], including perception, data processing, modeling, simulation, human–computer collaboration, and more. By constructing virtual models and simulations, DTs help people to gain a deeper understanding of complex physical entities and processes.

3.1. Virtual Reality Scene Design and Unity

Creating a virtual reality scene typically encompasses three primary steps: modeling, texturing, and rendering. Initially, utilizing modeling software, the shape, dimensions, and structure of an object or scene, along with other intricate details, are transformed into a 3D model. This involves sketching lines, creating surfaces, deforming shapes, and so forth, in order to define and sculpt the appearance and form of the subject. Subsequently, textures or graphic tools are employed to create and manipulate material maps, thereby infusing the model with surface nuances and hues, enhancing its verisimilitude and intricacy. Finally, the process culminates in rendering, where lighting, shadows, and other special effects are applied to the model, endowing it with a heightened sense of realism and vividness.

Unity [25] proffers an intuitive and user-friendly 3D modeling toolset, coupled with a robust graphics rendering engine that underpins high-quality visual effects. It facilitates the interactive and vivid presentation of complex data and information through 3D visualization, thus streamlining the construction of virtual environments for DTs. In addition, it empowers end-users to comprehend and analyze the contents of DTs more effectively. For instance, Unity boasts high-quality materials, illumination, and shadow effects, as well as supports for physical simulation and collision detection, thereby enhancing the realism of virtual environments. In contrast to open-source 3D graphics libraries such as Three.js, Unity efficiently manages components such as resource managers and scene editors, making it suitable for modeling in large-scale scenes and supporting subsequent system upgrades.

Therefore, Unity serves as the principal instrument for implementing the DT polder area system, including modeling the fundamental terrain utilizing the Terrain toolset; crafting textures with Paint Texture to generate effects such as grasslands, rocks, and trees; and leveraging the Bakery baking plugin to perform corresponding ambient lighting rendering operations for the scene, ensuring that the ultimate DT of the polder area possesses a realistic appearance.

3.2. Hydrological Mechanism Model and Data-Driven Model

DTs underscore the content of simulations, are capable of swiftly mirroring the changes in the physical world, and can utilize data feedback from physical entities for self-learning and enhancement. However, mechanism models are usually limited by their computation speed, requiring substantial computing resources and incapable of relearning from feedback data and experience from the physical world, necessitating adjustments based on human understanding of the data. On the other hand, purely data-driven models struggle to integrate physical laws and domain knowledge, resulting in constructed data models that lack interpretability. This is particularly true when dealing with nonlinear, multiscale physical systems, where the models exhibit low accuracy and severely deficient generalization capabilities [26]. Therefore, in the absence of sufficient conditions for constructing a physics-informed neural network [27, 28], it is a practical approach to comprehensively refer to the results calculated from different models. Here, the Xin’anjiang model and the N-BEATS model are, respectively, employed to forecast the hydrological status.

3.2.1. Xin’anjiang Model

The Xin’anjiang model [29] is a crucial and well-known hydrological mechanism model, which simulates and analyzes the hydrological processes of a watershed by considering factors such as precipitation, evaporation, runoff, infiltration, and storage. It has a wide range of applications in areas such as flood forecasting, drought assessment, and water resource management.

The main feature of the Xin’anjiang model is the concept that saturation-excess runoff occurs without further loss when the aeration zone reaches its field capacity [30]. The catchment is divided into a set of subcatchments, allowing for taking the spatial patterns of forcings and land surface conditions into account at the subcatchment level. For each subcatchment, runoff is calculated using four major modules: evapotranspiration module, runoff generation module, runoff separation module, and runoff routing module (Figure 1). In the runoff routing module, the overland flow directly flows into the river network of each subcatchment due to short, negligible concentration time, while the interflow and groundwater flow concentrate slowly; they first pass through the regulation and storage of the conceptualized linear reservoirs and then converge into the river network. Total runoff, i.e., the sum of surface flow, interflow, and groundwater flow, of each subcatchment is directly routed to the outlet of each subcatchment through the lag-and-route method. The outflow from each subcatchment is then routed along the main river reaches using the Muskingum successive routing scheme to produce the flow at the outlet of the whole catchment.

[figure(s) omitted; refer to PDF]

3.2.2. N-BEATS Model

The N-BEATS model [31, 32], proposed by Turing Award laureate Bengio and his team, is adept at tackling univariate time series forecasting tasks using deep learning. That is to say, given a historical sequence of length T, it predicts the values within the subsequent H windows, and its structure is shown in Figure 2.

[figure(s) omitted; refer to PDF]

The N-BEATS model is composed of multiple stack modules, each of which is formed by a series of blocks. The input for the first block is the original input sequence, and its output is twofold: one is the predicted values for the future window H and the other is the reconstructed value for the block’s input. The inputs for the subsequent blocks are all the residuals obtained by subtracting the reconstructed value from the previous block’s input. On the one hand, the next block acts as a complement to the preceding block, continuously fitting the residual information that the previous block did not capture. On the other hand, this process can be seen as a decomposition of the time series information, with different blocks in various stacks fitting certain parts of the time series information. Ultimately, the model’s output is the summation of the outputs from each stack.

Compared to the long short–term memory network (LSTM), the N-BEATS model, although also a method for modeling temporal data, exhibits significant differences. By incorporating a dual-residual design, the N-BEATS model performs information decomposition in a hierarchical manner, thereby effectively capturing both long-term and short-term patterns within sequences. This renders N-BEATS more adaptable and capable of efficiently modeling information across various temporal scales. In terms of interpretability, the N-BEATS model places a significant emphasis on incorporating distinct branches for sequence decomposition and residual prediction in its design, which facilitates enhancing the explicability of the model’s outputs. In addition, owing to its relatively simplistic internal structure, N-BEATS exhibits heightened efficiency during both training and inference phases.

Conversely, LSTM models may encounter issues such as gradient vanishing or gradient exploding when dealing with long sequences, leading to an increased demand for computational resources.

4. The Architecture of the DT Polder Area System

Taking the polder area as the specific research subject, the architecture of the DT polder area system is divided into five layers, with the specific structure delineated in Figure 3.

1. Physical object layer: The physical object layer refers to the actual physical objects in the objective world, mainly referring to the four elements of concern in the polder area: water body, water conservancy projects, weather, and terrain.

2. Data perception layer: The data perception layer is used to perceive various monitoring data in the polder area, including water level; flow rate and other data of water body; temperature, rainfall, and other meteorological information; and operation status data of water conservancy projects; as well as geographic information data. The data perception layer provides support for the real-time changes of DT scenes and the data needed to call the model.

3. Data processing layer: The data processing layer is primarily responsible for the processing and storage of data, mainly storing actual measurement data such as meteorological and water conservancy basics obtained from the data perception layer, as well as the predictive results of models in the model platform layer.

4. Model platform layer: The model platform layer is the core of the DT polder area system architecture, mainly including data-driven models represented by the N-BEATS model, mechanism models represented by the Xin’anjiang model, and visualization models of various elements. The models acquire the data from the data processing layer, call the prediction models to obtain the prediction results, and store the prediction results. It also provides support for the business application layer.

5. Business application layer: The business application layer is the top layer of the architecture of the DT polder system, providing specific applications and responsible for interacting with users. Here, the main functions include monitoring of the polder area, water level and flow rate prediction, waterlogging process rehearsal, and warnings for exceeding flood limit water levels.

[figure(s) omitted; refer to PDF]

5. The Methodology of Constructing the DT Polder Area System

5.1. Characterization of Elements

The landscape of the polder area is intricate, encompassing a multitude of elements. The primary focus of this study lies on the water body, terrain, weather, and water conservancy projects. The structural diagram of these elements is depicted in Figure 4, and the whole structure of the elements can be expanded on demand.

[figure(s) omitted; refer to PDF]

When depicting the elements of a polder area, it is necessary to carry out a data description of the structural elements of the polder area. The data format adopts JSON format, mainly for the following reasons: (1) JSON is an open data exchange format with a clear and concise hierarchical structure and (2) the related technologies of JSON have matured, and third-party libraries can be widely used for development. The JSON data and the corresponding 3D scene are shown in Figure 5. It shows a partial data description of the water body in the polder area, where each JSON data represent the state of the water body at a specific moment. When the 3D visualization model in the model platform layer receives real-time data, only the state of the corresponding elements will change, and the rest of the elements will remain unchanged until new data are received. By depicting the data of the elements and storing it as a universal and shareable JSON file, it provides a software-defined foundation for quickly building fine-grained DT polder area objects.

[figure(s) omitted; refer to PDF]

5.2. The Strategy of Integrating and Invocating Models

Whether it is a hydrological mechanism model or a data-driven model, each has its own pros and cons. In practical applications, combining different hydrological prediction models often results in more accurate results. Here, three strategies for integrating and invoking prediction models are proposed.

5.2.1. Combination of Bayesian Weighted Average

Bayesian weighted average refers to the calculation of the weights of different model results through Bayesian probability methods, and then taking these as a basis for weighted averaging, in order to obtain a more accurate and reliable combined forecast value. This method can be used for the combination of multiple model results, as well as for calculating the uncertainty of a single model or combined results.

Assuming Q represents the forecast results, $D=X,Y$ represents the actual measured data (where X denotes the input data and Y denotes the actual measured data), $f=f1,f2,\dots ,fn$ is the forecast set of n models. The principle of probability forecast in Bayesian weighted average is as follows:$$\begin{array}{}\text{(1)}& pQD={\displaystyle \sum }_{k=1}^{n}p{f}_{k}D·p_{k}Q{f}_k,D,\end{array}$$where$p{f}_{k}D$ is the posterior probability of the k-th model forecast $f_k$ given the observed data D, which reflects the degree of matching between $f_k$ and the measured flow rate Y. In fact, $p{f}_{k}D$ is also the proportion of weights in the weighted combination strategy for each model’s prediction result. The higher the accuracy of the model’s prediction results, the greater the weight obtained. In addition, the weight ratios of each model are all positive and the cumulative sum is 1. $p_{k}Q{f}_k,D$ is the posterior distribution of the forecast value Q given the forecast result $f_k$ of the model and the data D. The forecast result of this strategy is the weighted average of the forecast results of a single model.

5.2.2. Combination of Optimal Precision Indicators

This strategy dynamically calculates the error based on the model’s past predictions and real-time monitored data, selecting the model with the smallest error to calculate the next result. The precision indicators of hydrological models involve the error coefficient of the peak flow rate ($Q_e$), sum of squared errors (SSEs), and root mean square error (RMSE). The specific calculation formulas are as follows:$$\begin{array}{}\text{(2)}& Q_e=\frac{Q_{0,m}-Q_m}{Q_m},\text{(3)}& \text{SSE}={\displaystyle \sum }_{i=1}^N{Q_t-Q_{o,t}}^2,\text{(4)}& \text{RMSE}=\sqrt{\frac{1}{\mathrm{N}}{\displaystyle \sum }_{t=1}^N{Q_t-Q_{o,t}}^2,}\end{array}$$where $Q_t$ represents the real-time observed flow rate value; $Q_o$, t represents the model’s prediction flow rate value; $Q_o$, m represents the actual measured peak flow rate value in the basin; $Q_m$ represents the model’s prediction peak flow rate value; and N indicates the length of the time series of results.

The DT polder area system retrieves past measured data and model prediction data from the database and calculates the errors of different models. The reference priority for model error is $\text{RMSE}>\text{SSE}>Q_e$. If the model’s errors are all less than the threshold, then the model with the smallest RMSE error is called among all models and the call result is returned; if the errors of all models are greater than the threshold, it means that the calculation results of the model may not be able to predict the future state of the polder area well. The system will prompt the users that the calculation results of the current model may have large errors and allow the users to manually select the prediction model to invoke.

5.2.3. Combination of Feature Engineering

The third strategy is a combination of feature engineering. Here, the feature training model integrates the Xin’anjiang model with the N-BEATS model, leveraging hydrological features extracted from the Xin’anjiang model to provide high-quality input data for training the N-BEATS model. Key variables extracted include precipitation, evapotranspiration, soil moisture content, and runoff, which effectively reflect the hydrological dynamics of the basin. To capture long-term trends and short-term fluctuations, the extraction process also involves calculating moving averages and rates of change in the time series, ensuring the model’s adaptability to diverse hydrological conditions.

After feature extraction, these characteristics are integrated into the N-BEATS model. During the construction of the input layer, features extracted from the Xin’anjiang model serve as inputs, enabling the N-BEATS model to fully utilize this information for learning and generating accurate predictions. This approach allows the N-BEATS model to focus not only on statistical features but also to incorporate physical characteristics, maintaining consistency with hydrological principles. Consequently, through feature extraction and hybrid model training, the model’s generalization capability is enhanced, and its adaptability to varying hydrological conditions is improved, offering a powerful tool for water resource management and decision support. The flowchart of the strategy using the combination of feature engineering is showed in Figure 6.

[figure(s) omitted; refer to PDF]

5.3. Construction and Presentation of the Visualization Model

The visualization model of the DT polder area is composed of five layers stacked on top of each other, as shown in Figure 7. The five-layer structure is as follows:

1. Terrain: Combining the elevation data of the polder area, the Terrain plugin in Unity is used to model the basic terrain of the polder area. Since the terrain layer only contains the elevation information of the polder area, the constructed 3D visualization model is a white model.

2. Trees and rocks: Currently, trees and rock layers are not included in the definition of the DT polder system. They primarily serve to represent the environment and decoration of the polder area, making the 3D visualization model more similar to the real world. By combining satellite imagery and using the Paint Texture tool to create textures, different regional textures are attached to the white film to construct the basic model of the DT polder area.

3. Water body: Due to the gentle terrain and the small change in elevation, the water surface can be regarded as the same horizontal plane. Therefore, the water body is mainly composed of a huge horizontal plane. The script is written to make the water body visually the same as the real river network, while providing a data interface to ensure that it can receive data transmitted by the prediction model, updating the flow rate and water level of the water body.

4. Water conservancy projects: Water conservancy projects are artificially constructed water conservancy facilities and infrastructure in polder areas, such as gates, pumps, and electricity towers. 3Dmax software is used to model the water conservancy projects in the polder area. After importing the built architectural models into Unity, it is necessary to write scripts for them and animate their motions. At the same time, Unity’s particle effect system can be used to create special effects.

5. Weather: Weather mainly includes sunny days, rain, snow, thunder and lightning, and other various weather conditions. Using the plug-in UniStorm, the effect is constructed for the entire system, enabling the system to represent various weather conditions according to the actual conditions.

[figure(s) omitted; refer to PDF]

In order to drive the visualization models of the DT polder area to show the states of the polder area in the objective world simultaneously, the key point is to focus on the real-time monitoring data transmitted by the data processing layer and then present the corresponding visual representation. To be more specific, first, the data perception layer stores real-time collected hydrological, water quality, weather, and other data from various stations. Then, it retrieves the real-time data, organizes it into JSON format, and then passes the structured JSON data to the model platform layer. The model platform layer parses the incoming data, analyzes the elements that need to be changed in the visualization model, and then calls the script interface provided during the visualization model construction for corresponding visual representation, such as the rising water levels and changing water colors. When the system invokes the prediction models, the visualization models also analyze the JSON data passed for corresponding visual representation. The difference is that these JSON data are no longer composed of real-time data but rather data returned by the prediction model called by the system.

6. System Implementation and Experiments

6.1. System Implementation

Currently, the DT polder area system has already implemented many key functions, including the following:

1. Real-time monitoring. By deploying sensors and monitoring equipment in the polder area, real-time collection of hydrological information such as water level and flow rate and status information of water conservancy projects and weather data are carried out. They are displayed dynamically on the system’s monitoring interface. Users can view the current water level, flow rate, and other information about the polder area at any time.

2. Prediction. Based on hydrological data, weather data, and other various information sources, the integration of N-BEATS and Xin’anjiang models is used to predict water level and flow rate for the upcoming period. Through the prediction results, the system can anticipate potential hydrological changes in the polder area in advance, providing a reference basis for related decision-making.

3. Prewarning. Based on real-time monitoring data and prediction, combined with warning rules and thresholds, the system continuously monitors and analyzes hydrological data. Once an abnormal situation exceeding the warning threshold is detected, the system will automatically issue a warning message to remind relevant personnel to take timely measures to deal with potential risks.

4. Rehearsal. Through visualization models, based on the results of the prediction models, the system can simulate and evaluate the water level or flow rate in the polder area. Through scenario rehearsal, the system can help relevant departments and personnel better understand potential risks and formulate corresponding preventive measures and plans. The rehearsal process of the decline of water level in the polder area is shown in Figure 8.

[figure(s) omitted; refer to PDF]

6.2. Experiment and Discussion

To verify the usability and effectiveness of the proposed DT polder area system, a series of experiments are conducted to collect system performance data. Subsequently, the system is also compared with other systems in terms of functionality.

6.2.1. Combination of Bayesian Weighted Average

The DT polder area system is deployed on a cloud cluster, and the software and hardware configuration parameters are shown in Table 1.

Table 1

Experimental environment.

Attributes	Values
CPU	Intel Xeon Platinum 2.6 GHz, 4 core
Memory	16 GB
Operation system	CentOS 7.6
Vue	Version 3.0
Unity	Version 20221.1f1c1

Experimental data include hydrological, topographical, weather, and water conservancy project-related data from a polder area in the Lixiahe river network of Jiangsu, China.

6.2.2. Combination of Bayesian Weighted Average

The performance metrics for the DT polder area system under different scenarios mainly adopted two indicators: GPU utilization rate and frames per second (FPS), where FPS refers to the number of image frames rendered and played by the system in one second. There are five main scenarios: (1) daily monitoring, (2) waterlogging, (3) opening the sluice to release water, (4) heavy rain, and (5) heavy snow. The results are shown in Table 2 below, with the results being the average of five test runs.

Table 2

Experimental results in different scenarios.

Scenarios number	Scenarios	GPU utilization rate (%)	FPS
1	Daily monitoring	45.7	120.4
2	Waterlogging	48.3	105.3
3	Opening the sluice to release water	50.2	101.7
4	Heavy rain	55.7	78.3
5	Heavy snow	55.3	81.2

From Table 2, it can be seen that in Scenario 1, the rendering efficiency is high, with the FPS basically maintaining around 120 frames, and its GPU utilization rate is 45.7%, consuming very few system resources. When simulating situations such as rainfall and waterlogging that cause changes in a water body, the FPS of the DT polder area system will gradually drop to around 105 frames. When particle effects are enabled to display weather conditions such as heavy rain and snowfall, the FPS of the DT polder area system will decrease, reaching around 80 frames, and the GPU utilization rate will slightly increase to 55%. In summary, under the current relatively common hardware configuration conditions, the smoothness of running various scenarios of the constructed DT polder area system can still be maintained within a satisfactory range.

6.2.3. Validation of the Accuracy of the Models

Assessing the accuracy of the system’s prediction models [33] for water level and flow rate is important. Here, four indicators are used for quantitative analysis of the predictive results: mean absolute error (MAE), mean absolute percentage error (MAPE), RMSE, and Nash–Sutcliffe efficiency (NSE). In this context, MAE is used to measure the overall predictive ability of the model. When the value of MAE is small, it means that the average prediction error of the model is small, and the model has a better predictive ability on the whole. MAPE measures the average percentage error between the predicted value and the actual observed value, which is used to measure the relative predictive ability of the model. RMSE pays more attention to the impact of large errors and is mainly used to measure whether there are extreme error values in the model’s prediction results. The smaller the numerical values of RMSE, MAE, and MAPE, the smaller the prediction error of the model. Conversely, NSE gauges the predictive capability of a model. When values are closer to 1, it denotes more accurate fits and greater model reliability. The calculation formulas are as follows:$$\begin{array}{}\text{(5)}& \text{MAE}=\frac{1}{n}{\displaystyle \sum }_{i=1}^n{Y}_i-X_i,\text{(6)}& \text{MAPE}=\frac{1}{n}{\displaystyle \sum }_{i=1}^n\frac{Y_i-X_i}{Y_i}\mathrm{\ast }100\%,\text{(7)}& \text{RMSE}=\sqrt{\frac{1}{n}{\displaystyle \sum }_{i=1}^n{Y_i-X_i}^2},\text{(8)}& \text{NSE}=1-\frac{{{\displaystyle \sum }}_{i=1}^n{Y_i-X_i}^2}{{{\displaystyle \sum }}_{i=1}^n{Y_i-\overline{Y}}^2},\end{array}$$where $Y_i$ is the actual measured value, $X_i$ is the model’s predicted value, $\overline{Y}$ is the actual average value, and n is the length of the data. The accuracy of the models is listed in Table 3.

Table 3

Accuracy index of different prediction models.

Date type	Index	Single model		Combined model
		Xin’anjiang model	N-BEATS model	Bayesian weighted average	Optimal precision indicators	Feature engineering
Water level	RMSE	1.425	1.288	0.825	1.191	0.867
	MAE	0.366	0.412	0.267	0.444	0.294
	MAPE	0.282	0.297	0.223	0.277	0.285
	NSE	0.683	0.751	0.812	0.695	0.803
Flow rate	RMSE	0.511	0.725	0.282	0.483	0.278
	MAE	3.02	3.17	2.62	2.52	2.60
	MAPE	0.419	0.336	0.121	0.133	0.118
	NSE	0.591	0.705	0.754	0.718	0.824

From Table 3, it is evident that in water level prediction, the N-BEATS model’s MAE and MAPE values are slightly higher than those of the Xin’anjiang model, indicating that the N-BEATS model performs slightly better in water level prediction. In addition, the N-BEATS model’s higher NSE value compared to the Xin’anjiang model further confirms its superior performance in overall water level prediction accuracy. Therefore, in the Bayesian combination strategy of the two models, N-BEATS should have a greater weight. By comparing the results of the two models on water level and flow predictions, the MAPE value of the model for water level prediction is higher than that for the flow rate prediction, suggesting that the model has superior capability in water level prediction. Moreover, when comparing the NSE values for flow rates, N-BEATS again outperforms Xin’anjiang.

Comparing the prediction indicators of the two combination methods, it can be found that the parameters of the Bayesian weighted average combination have improved compared to the single model, including a notable improvement in NSE, indicating that introducing Bayesian weights into different models effectively improves overall prediction accuracy. Similarly, the feature engineering method also demonstrates a strong performance with high NSE values, making it a viable alternative for improving prediction accuracy. However, for the precision index combination method, although there is a significant improvement in the MAE value and MAPE value of the flow, the improvement of other parameters, including NSE, is not obvious, which indicates that there is still room for improvement in the effect of this combination method, providing a reference for users to reasonably choose the prediction model.

6.2.4. Comparison Between Systems

Although DT technology has been applied in the field of water conservancy, the current DT systems lack the ability to integrate monitoring, forecasting, simulation, and control functions into a unified whole. Most systems focus on a single aspect of functionality, such as the DT systems implemented for the Canal de Garonne by Ranjbar, respectively. Ranjbar’s system achieved monitoring and forecasting for the canal, while Fonseca’s system simulated the forecast results. However, both neglected the impact on user decision-making.

Through the weather monitoring, forecasting, and simulation functions demonstrated in Section 6.1 of the DT polder area system, in addition to the basic functions of monitoring, forecasting, and simulation, the DT polder area system also integrates multiple models to enhance the prediction, thereby better-supporting user decision-making. Table 4 shows a comparison of the functionalities of the DT polder area system with other systems. Clearly, the proposed system is more comprehensive.

Table 4

Comparison of various DT systems in the water conservancy field.

Function	DT polder area system	Canal of Calais [18]	Wu’s System [20]	DT model [15]
Monitoring	✓	✓	✓	✓
Prediction	✓	✓	✓	✓
Simulation	✓	✗	✓	✗
Environment	✓	✗	✗	✗

7. Conclusions

This study proposes a DT polder area system, with a focus on data representation of key elements in polder areas such as water bodies, water conservancy projects, weather, and so on. A 3D virtual polder area system is constructed based on Unity, integrating the Xin’anjiang model and the N-BEATS model to predict water level and flow rate, thereby driving scenario simulations to anticipate potential impacts of precipitation and waterlogging. The experimental results also demonstrate the usability and effectiveness of this solution, offering a reference for the construction of DT systems or scenarios in the current field of water conservancy.

In the future, our work will focus on two main directions: First, we will delve into how to integrate mechanism models, data models, and knowledge models, thereby providing support for the construction of high-fidelity scenarios. Second, we will explore lightweight scenario construction techniques, integrating the DT polder area system with the larger DT water network.

Funding

This study was funded by the National Key Research and Development Program of China (2022YFC3202600), the Major science and technology project of the Ministry of Water Resources (SKS-2022139), and the Water Conservancy Science and Technology Project of Jiangsu Province (2022003).

Acknowledgments

This study was funded by the National Key Research and Development Program of China (2022YFC3202600), the Major science and technology project of the Ministry of Water Resources (SKS-2022139), and the Water Conservancy Science and Technology Project of Jiangsu Province (2022003).

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