Advertisement
Browse Subject Areas
?

Click through the PLOS taxonomy to find articles in your field.

For more information about PLOS Subject Areas, click here.

  • Loading metrics

Open Access

Peer-reviewed

Research Article

RETRACTED: The artificial intelligence-based agricultural field irrigation warning system using GA-BP neural network under smart agriculture

  • Xiying Wang

    Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft

    404564527@qq.com

    Affiliation School of Civil and Architectural Engineering, Harbin University, Harbin, China

    ⨯

Retraction

The PLOS One Editors retract this article [1] due to concerns about potential manipulation of the publication process. These concerns call into question the validity and provenance of the reported results. We regret that the issues were not identified prior to the article’s publication.

The author either did not respond directly or could not be reached.

23 Feb 2026: The PLOS One Editors (2026) Retraction: The artificial intelligence-based agricultural field irrigation warning system using GA-BP neural network under smart agriculture. PLOS ONE 21(2): e0343197. https://doi.org/10.1371/journal.pone.0343197 View retraction

Abstract

This work explores an intelligent field irrigation warning system based on the Enhanced Genetic Algorithm—Backpropagation Neural Network (EGA-BPNN) model in the context of smart agriculture. To achieve this, irrigation flow prediction in agricultural fields is chosen as the research topic. Firstly, the BPNN principles are studied, revealing issues such as sensitivity to initial values, susceptibility to local optima, and sample dependency. To address these problems, a genetic algorithm (GA) is adopted for optimizing the BPNN, and the EGA-BPNN model is used to predict irrigation flow in agricultural fields. Secondly, the EGA-BPNN model can overcome the local optimization and overfitting problems of traditional BPNN through the global search ability of GA. Moreover, it is suitable for the irrigation flow prediction task with complex environmental factors in smart agriculture. Finally, comparative experiments compare the prediction accuracy of BPNN and EGA-BPNN using single and dual water level flow prediction models respectively. The results reveal that as the number of nodes in the hidden layer increases, the model’s Mean Squared Error (MSE) and Relative Error (RE) show a decreasing trend, indicating an improvement in model prediction accuracy. When the number of nodes in the hidden layer increases from 6 to 16, the MSE of the single and dual water level flow prediction models decreases from 4.53×10−4 to 3.68×10−4 and 2.38×10−4 to 1.66×10−4, respectively. Under a standalone BPNN, the absolute relative error in flow prediction is 1.09%. In contrast, the EGA-BPNN model achieves a significantly lower mean absolute relative error of 0.41% for single-flow prediction, demonstrating superior prediction performance. Furthermore, compared to the BPNN, the EGA-BPNN model exhibits a 2.11 reduction in MSE, further emphasizing the positive impact of introducing the GA on model performance. The research outcomes contribute to more accurate water resource planning and management, providing a more reliable basis for decision-making.

Citation: Wang X (2025) RETRACTED: The artificial intelligence-based agricultural field irrigation warning system using GA-BP neural network under smart agriculture. PLoS ONE 20(1): e0317277. https://doi.org/10.1371/journal.pone.0317277

Editor: Morteza Taki, Agricultural Sciences and Natural Resources University of Khuzestan, ISLAMIC REPUBLIC OF IRAN

Received: October 15, 2024; Accepted: December 23, 2024; Published: January 17, 2025

Copyright: © 2025 Xiying Wang. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the paper and its Supporting information files.

Funding: This work was supported by the Science and Technology Innovation Team of Harbin University, 2023 Science and Technology plan self-financing project of Harbin under Grant No. 2023ZCZJCG023, awarded to XW. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

1 Introduction

1.1 Research background and motivations

With the rapid advancement of technology, smart agriculture has attracted widespread attention as a significant innovation in the agricultural sector. Smart agriculture integrates information technology, sensor technology, and advanced decision support systems to enhance agricultural production efficiency, reduce resource waste, and adapt to the growing global demand for food [1]. In this information age, the digital transformation of agriculture has become a key factor in ensuring food security and sustainable development. As global climate change intensifies, agriculture faces increasing challenges, with water scarcity being one of the most pressing issues. Irrigation, as a crucial component of agricultural production, directly affects farmland yield and quality [2, 3]. Improving irrigation efficiency has become a critical priority in the agricultural sector to optimize water resource utilization. To address these challenges, smart agriculture can use advanced prediction models, especially those based on deep learning and optimization algorithms. These models can process high-dimensional multi-source data and capture complex non-linear relationships, thereby improving the prediction accuracy of irrigation flows and optimizing water resource allocation [4, 5].

As a crucial component of smart agriculture, the agricultural field irrigation warning system offers farmers precise, science-driven decision support for irrigation. Integrating advanced sensor technology, big data analytics, and artificial intelligence (AI) algorithms can monitor soil moisture, meteorological conditions, and other factors in real-time. This enables the dynamic adjustment of irrigation plans, minimizing waste and maximizing water resource efficiency [6, 7]. In the agricultural field irrigation warning system, the prediction model for irrigation flow plays a critical role. By analyzing historical data and considering different meteorological and soil conditions, this model predicts future irrigation needs to provide the system with rational irrigation plans [8–10]. Consequently, the irrigation flow prediction model’s precision and robustness directly impact the effectiveness of the entire agricultural field irrigation warning system.

In this context, the Backpropagation Neural Network (BPNN) model, as a common type of artificial neural network (ANN), is widely applied to various prediction tasks. However, BPNN has some limitations in practical applications, such as sensitivity to initial values, susceptibility to local optimal solutions, and dependency on specific samples [11]. To address these issues, this work proposes an Enhanced Genetic Algorithm—Backpropagation Neural Network (EGA-BPNN) model that optimizes the BPNN structure through Genetic Algorithm (GA). GA, by simulating the processes of natural selection and genetic recombination, effectively explores the parameter space, thus overcoming the traditional BPNN’s sensitivity to initial values. Specifically, GA optimizes the initial weights of BPNN, making the model’s training process less likely to fall into local optimal solutions, thereby enhancing its global search capability [12]. Additionally, GA’s global search characteristics can effectively avoid the overfitting issues that BPNN may encounter during training due to over-reliance on specific samples, thus improving the model’s robustness and generalization ability [13]. By integrating GA with BPNN, the EGA-BPNN model can accurately predict agricultural irrigation flow under complex environmental conditions, thereby enhancing the efficiency and prediction accuracy of agricultural water resource utilization.

1.2 Research objectives

The core issue of this work is how to utilize advanced AI technologies to accurately predict irrigation demand for farmland under different environmental conditions, thereby achieving rational allocation and efficient conservation of water resources in the context of smart agriculture. The research process emphasizes the crucial role of precision irrigation in improving agricultural productivity and promoting sustainable agricultural development. The primary research objective is to construct an efficient model for predicting agricultural field irrigation flow by combining GA with BPNN, aiming to enhance the irrigation efficiency of smart agriculture systems. Hence, this work investigates the principles and issues of the BPNN, selects GA to optimize the BPNN, and constructs an EGA-BPNN model for predicting agricultural field irrigation flow. The model’s performance is validated through comparative experiments, using relative error (RE), mean squared error (MSE), and mean squared absolute error (MSA) as indicators for model prediction performance. This work can provide valuable insights and references for studies and applications in related fields.

2 Literature review

Since this is the era of big data, research on prediction methods using deep learning models has garnered widespread attention. Chen et al. (2021) proposed an irrigation decision-making method based on deep Q-learning (DQN), which combined short-term weather forecasting to optimize the water use efficiency of rice planting. Compared with traditional irrigation, DQN irrigation saved an average of 23 millimeters of irrigation water, mitigated drainage by 21 millimeters, and reduced irrigation frequency by 1. Meanwhile, it could maintain yield level, providing an effective solution to handle weather forecast uncertainty [14]. Sadeghi Gargari et al. (2022) employed the long-term freight rate forecasts from the 10-year strategic plan of Iran’s largest port, Rajaei Port. They used Seasonal ARIMA (SARIMA) and neural network models to predict container ship traffic at the port between 2020 and 2025 [15]. Similarly, Suresh (2021) introduced a hybrid approach combining ARIMA and neural networks for electricity consumption forecasting using smart meter data. After evaluation, it was found that the Mean Absolute Percentage Error (MAPE) of this model in the test was 25.53, the accuracy was 48.38, and the MSE was 0.21, which was better than similar methods [16]. Guo et al. (2022) proposed a hybrid model that combined seasonal autoregressive integrated moving average and denoising autoencoder (SARIMA–DAE) to predict atmospheric temperature profile. Experimental results showed that MSE on the test set was 0.12, MAPE was 0.0012, and the absolute error was within 1K. Compared with the traditional model, the SARIMA–DAE model’s prediction accuracy in each altitude layer was improved [17].

In the field of smart agriculture, there are also various prediction models. Hamrani et al. (2020) compared three categories of machine learning (ML) models, classical regression, shallow learning, and deep learning, to predict agricultural soil greenhouse gas emissions. They found that the Long Short-Term Memory (LSTM) network performed the best in predicting soil greenhouse gas emissions in a farmland in Quebec, Canada. The R coefficient for CO2 flux prediction was 0.87 with an RMSE of 30.3 mg·m−2·hr−1. For N2O flux prediction, the R coefficient was 0.86 with an RMSE of 0.19 mg·m−2·hr−1, providing a new perspective on the application of ML models in predicting environmental greenhouse gas emissions [18]. Sumathi et al. (2022) proposed a smart agriculture system that utilized Internet of Things (IoT) sensors, fuzzy association rules, and ANNs to classify, analyze, and securely transmit agricultural field data. This system enhanced crop yield and profits and implemented secure and traceable agricultural management using blockchain technology [19]. Rashid et al. (2021) summarized the application of ML in crop yield prediction, focusing on palm oil production forecasting, and proposed key challenges and prospects for future development [20].

In recent years, research on agricultural irrigation warning systems based on Gaa and BPNN in the context of smart agriculture has gained widespread attention in the academic community. Zhang and Qu (2021) optimized BPNN using an Adaptive Genetic Algorithm (AGA), expanding its application in nonlinear problems [21]. They found that the optimized AEGA-BPNN algorithm significantly outperformed traditional BPNN models in computational accuracy and generalization performance, particularly in traffic flow prediction tasks. However, they noted challenges in maintaining population diversity during the later stages of evolution, limiting its optimization effectiveness. Chen et al. (2019) proposed an Improved Genetic Algorithm (IGA) combined with BPNN for water level prediction [22]. Their findings showed that IEGA-BPNN mitigated issues of local optima and local convergence when dealing with complex neural networks. The experimental results show that the MSRE of IEGA-BPNN is 0.031, which is better than 0.037 for EGA-BPNN and 0.045 for ANNs compared with traditional EGA-BPNN. Alfred (2015) compared the performance of BPNN and GA-optimized BPNN (EGA-BPNN) in time series data prediction [23]. The results indicate that the MSE of EGA-BPNN is 0.054, which is lower than the prediction accuracy of traditional BPNN, highlighting the significant improvement in prediction accuracy. Shen et al. (2020) investigated the application of GA-optimized BPNN in predicting the speeds of Hybrid Robotic Fish [24]. Their findings indicated that the EGA-BPNN model exhibited higher prediction accuracy and efficiency in complex marine environments, thus validating its feasibility. Xia et al. (2022) proposed a model for estimating Cultivated Land Quality (CLQ) based on Gradient Boosting Decision Tree (GBDT) and EGA-BPNN [25]. The study demonstrated higher accuracy in CLQ estimation, particularly when using seven optimal crop phenological indicators, significantly improving the precision of CLQ estimation and reducing the normalized root mean square error of CLQ by 3.17%. Zhao et al. (2018) conducted predictive studies on the anaerobic digestion of wastewater. They found that EGA-BPNN outperformed traditional BPNN models in predicting Chemical Oxygen Demand (COD) and gas production. The MAPE and MSE of EGA-BPNN are 20.9854% and 7.5677%, respectively, better than BPNN’s 60.7234% and 10.5521% [26].

Although the above studies indicate significant optimization effects and prediction performance of the EGA-BPNN model in various fields, there are still some limitations. Firstly, many neural network-based models, such as the BPNN, suffer from sensitivity to initial weights and threshold values, which can easily lead to suboptimal solutions, resulting in low model training efficiency and unstable prediction accuracy. Additionally, while GA possesses global search capabilities in optimizing neural networks, its traditional optimization processes may face issues of slow convergence and premature convergence when handling complex systems, limiting further model optimization and performance enhancement. Secondly, existing models often lack sufficient robustness and generalization ability, especially in prediction tasks under dynamic and complex environments, where they are susceptible to the influence of data fluctuations and noise. These limitations are particularly pronounced in smart agriculture, as agricultural irrigation involves complex and variable environmental factors, requiring models to have higher adaptability and precision. To solve these problems, this work introduces the EGA-BPNN model into the smart agriculture field to explore new methods for predicting agricultural irrigation flow. The EGA-BPNN model combines the advantages of GA and BPNN and significantly improves the model’s global search ability and training efficiency by optimizing the initialization weights and thresholds of BPNN. Based on the GA algorithm, more effective encoding strategies and mixed selection mechanisms are introduced to avoid the problems of local optima and premature convergence in traditional methods. The research findings enhance the accuracy of water resource planning and management, providing more reliable decision-making foundations with significant theoretical and practical implications.

3 Research model

3.1 Analysis of the BPNN principle

The BPNN is an ANN based on the BP algorithm, which adjusts and optimizes the connections between neurons in multiple layers to achieve data classification and prediction [27, 28]. Fig 1 depicts a common structure of the BPNN.

thumbnail
Download:
Fig 1. Structure of BPNN.

https://doi.org/10.1371/journal.pone.0317277.g001

The fundamental architecture of the BPNN, as depicted in Fig 1, comprises the input, hidden, and output layers. Each unit in a lower layer is fully connected to every unit in the next layer, while neurons within the same layer remain independent, with no intra-layer connections. The adjacent neurons in two consecutive layers are connected through adjustable weight connections, and there is no feedback between neurons [29]. Assuming the input vector is A = [a1, a2, ⋯, an], the input layer receives input signals and transmits them to the hidden layer. The hidden layer performs a non-linear transformation on the input signals and passes the transformed results to the next hidden layer or the output layer, as shown in Eq (1) [30, 31].

(1)

hl represents the output of the hidden layer in the l-th layer; σ(⋅) denotes the activation function; Wl and bl refer to the weight matrix and bias vector of the l-th layer, respectively. The output layer performs a non-linear transformation on the output of the hidden layer, and the transformed result serves as the final output, represented as: (2)

z refers to the output of the output layer. Finally, the error between the output and the expected output is calculated, and backpropagated to the weights of each layer to update the weights. The error function is as follows: (3)

y represents the expected output, and E(⋅) refers to the error function. The calculation method for backpropagating the error reads: (4)

represents the connection weight between the j-th neuron in layer l and the i-th neuron in layer l-1.

3.2 The Problems of the BPNN

While the BPNN performs well in many applications, it encounters practical challenges: sensitivity in the selection of initial values, susceptibility to local optima, and sample dependence [32–35].

  1. The selection of initial weights and biases significantly influences the BPNN’s performance. Different initial values make the network converge to various local optima, affecting the model’s generalization ability. Poor initial value choices may cause the training process to encounter a gradient plateau prematurely, hindering further learning [36–38].
  2. BPNN adopts the steepest descent method for layer-wise training, which updates weights based on local gradients However, this method is prone to being trapped in local optima, preventing it from finding the global optimum. Particularly, in high-dimensional spaces, numerous local optima exist. The BPNN training process may be influenced by initial values and data distribution, resulting in being stuck in local optima and failing to find better solutions [39–41].
  3. The performance of the BPNN is sensitive to the order and distribution of training samples. Different sample orders may lead the network to learn various features, impacting the model’s generalization performance. If the training samples are insufficient or not representative, the network may suffer from overfitting, leading to poor performance on unseen data [42–44].

To overcome these issues, researchers have proposed various improvement methods, including adopting advanced optimization algorithms, employing alternative activation functions, and adjusting learning rates [45–47]. For instance, employing random initial values, utilizing advanced optimization algorithms (such as GA, ant colony algorithms, and evolutionary algorithms), and introducing regularization techniques are common improvement strategies to improve the BPNN’s training stability and generalization capability. This work selects GA to enhance the BPNN.

3.3 EGA-BPNN model

The GA is an optimization algorithm that simulates natural selection and genetic mechanisms, designed to find a global or approximate optimal solution for a given problem [48–50]. Its fundamental idea is to emulate the process of natural selection and genetic mechanisms observed in biological evolution. The algorithm gradually improves the current solution’s quality by simulating a population’s evolution to seek the optimal solution for the problem [51, 52]. The algorithm mirrors the processes of natural selection and genetic mechanisms, evolving candidate solutions through operations such as genetic inheritance, crossover, and mutation, aiming to discover an optimized solution for the problem [53, 54].

Optimizing a BPNN through GA involves constructing the basic BPNN and then applying GA to refine the initial weights and thresholds of the neural network. GA is employed to search for the globally optimal combination of weights and thresholds, thus enhancing the neural network’s performance [55–57]. Fig 2 illustrates the flowchart of the optimized EGA-BPNN model.

thumbnail
Download:
Fig 2. Algorithm flow of the GA-BPNN model.

https://doi.org/10.1371/journal.pone.0317277.g002

Fig 2 reveals that the GA-BPNN model primarily consists of the following three steps:

  1. Determination of the encoding of weights and thresholds: In GA, the expression form of an individual is described by genes. For the GA-BPNN algorithm, genes are typically used to represent the neural network’s weights and thresholds, constituting the BPNN structure and determining its relevant parameters.
  2. Estimation of individual fitness: Estimating individual fitness is a crucial step in GA, and it evaluates each individual’s performance in problem-solving. In the GA-BP algorithm, individual fitness is assessed using the BPNN. Specifically, based on the individual’s gene encoding, a neural network model is constructed. The model’s error is calculated using training data, and this error is considered as the individual’s fitness. A smaller fitness value indicates better individual performance.
  3. Application of evolutionary operators: Evolutionary operators include selection, crossover, and mutation operations, simulating the biological evolution process to optimize individuals continuously. In the GA-BP algorithm, the selection process favors individuals with higher fitness, preserving their genetic information. The crossover operation generates new individuals by exchanging genetic material, while mutation introduces random gene variations. These evolutionary operations iteratively refine the genetic information, steering the population toward optimal solutions and effectively optimizing the neural network’s weights and thresholds.

This work addresses the EGA-BPNN model’s susceptibility to local optima and slow convergence during the initialization of weights and thresholds, which limits its widespread application in complex systems such as smart agricultural irrigation warning systems. To address these issues, an EGA has been introduced. EGA optimizes the initialization of BPNN weights and thresholds by employing more efficient encoding strategies and selection mechanisms, accelerating convergence, enhancing global search capabilities, and reducing the risk of being trapped in local optima. EGA uses floating-point encoding during the encoding stage to accurately represent weights and thresholds. It introduces a hybrid strategy in crossover and mutation operations to balance exploration and exploitation, maintaining population diversity and preventing premature convergence. Applying EGA to initialize BPNN, through multiple generations of iterations, this work employs a network performance-based fitness function to evaluate each individual. Ultimately, it identifies an optimized set of weights and thresholds that serve as the starting point for network training. The flow of the EGA-BPNN is depicted in Fig 3.

thumbnail
Download:
Fig 3. The workflow of EGA-BPNN.

https://doi.org/10.1371/journal.pone.0317277.g003

This improvement notably enhances BPNN’s training efficiency and prediction accuracy, providing a stronger and more reliable model foundation for smart agricultural irrigation warning systems.

3.4 Model evaluation indicators

Models are typically evaluated based on their prediction accuracy. Essentially, the so-called prediction accuracy is the degree of deviation between predicted and actual values. The closer the predicted value is to the actual value, the higher the prediction accuracy. This work selects RE, MSE, and MSA as measurement indicators for the prediction performance of the model, and their calculation is as follows [58, 59]: (5) (6) (7)

yi refers to the real value, is the value predicted by the model, and n represent the sample quantity. The smaller the values of RE, MSE, and MSA, the closer the model’s predictions are to the actual observed values, indicating better model performance.

4 Experimental design and performance evaluation

4.1 Datasets collection

Actual data obtained from precise measurements of natural trapezoidal channels in farmland in a certain area are used as sample data. Fig 4 displays some specific data points.

thumbnail
Download:
Fig 4. Example of sample data.

https://doi.org/10.1371/journal.pone.0317277.g004

Fig 4 illustrates the actual water levels and flow rates within the irrigation area of farmland in a certain region. Data obtained through the velocity-area method are utilized to train and simulate the neural network. Fifty groups of randomly selected data are used for training, with 15 additional samples reserved for testing. To further demonstrate the EGA-BPNN model’s potential and robustness, the dataset is expanded to include complex meteorological conditions, such as extreme temperatures, varied precipitation patterns, and fluctuating humidity levels. These conditions are critical for intelligent farmland irrigation systems, as they directly affect crop water requirements and soil moisture retention. These conditions are crucial for intelligent farmland irrigation systems because they directly affect crop water requirements and soil moisture retention capacity. In addition, data are acquired on different soil types, including sandy, clay, and loam soils, each with unique water infiltration and evaporation properties. The diversity of these data allows the model to learn the impact of different soil types on irrigation needs and considers the varying water requirements of different crops at different growth stages. For instance, crops like wheat, corn, and soybeans exhibit distinct water needs, which also vary across their growth cycles. By collecting data on crops including but not limited to wheat, corn, and soybeans, the model can better understand and predict the irrigation needs of different crops at various growth stages. The data sources include figshare - credit for all your research and nesdc.org.cn. The dataset encompasses various environmental parameters such as temperature, humidity, and soil moisture. The temperature directly affects the transpiration rate and the efficiency of photosynthesis in crops, which in turn influences their water requirements [60, 61]. Humidity reflects the water vapor content in the air, where lower humidity usually means higher evaporation rates, thereby increasing the crop’s irrigation needs. Soil moisture, a key determinant of water availability to crop roots, is also critical. Additionally, data on soil types, ranging from sandy to clay soils, are included to capture variations in water infiltration and evaporation characteristics, enabling the development of more precise irrigation strategies. Considering the different water requirements of crops at diverse growth stages, data are collected for wheat, corn, and soybeans. These data help the model understand changes in irrigation needs throughout the crop growth cycles, leading to more accurate irrigation predictions.

In terms of data preprocessing, this work undertakes the following steps to ensure data quality and the effectiveness of model training. Initially, raw data are cleaned to remove outliers and missing values, ensuring data integrity and accuracy. Outlier treatment employs the boxplot and Z-score methods, setting thresholds to eliminate extreme values that deviate significantly from the normal data distribution. Missing value treatment involves selecting different imputation methods based on the type of data and the proportion of missingness, such as using mean filling, interpolation, or speculative filling strategies based on similar data. This effectively avoids interference from missing values in model training. Subsequently, all data undergoes standardization processing using the Z-score standardization method, setting the mean of each feature to 0 and the standard deviation to 1, to eliminate the impact of different dimensions and units. Standardized data allows all features to be trained on the same scale, preventing certain features from having an imbalanced influence on model training due to their large or small numerical values. Additionally, feature engineering is performed, encompassing feature selection and construction, to extract the environmental parameters most influential for irrigation demand prediction. Feature selection is conducted through correlation analysis to identify the features most relevant to irrigation demand, removing redundant and unimportant variables. Feature construction includes generating new features based on raw data, such as creating features based on seasonal variations from historical meteorological data, or building interaction features based on the relationship between soil moisture and temperature. These new features help improve the model’s prediction performance. Finally, the dataset is divided into training, validation, and test sets, with cross-validation employed to assess the model’s stability and generalization ability.

4.2 Experimental environment and parameters setting

The experiment is conducted on a 64-bit Windows 10 operating system with NVIDIA GeForce RTX 2070 graphics processor. The Center Processing Unit (CPU) is Intel® Core™ i7-8700K CPU @3.70GHZ, with a memory of 32GB. The simulation is conducted on MATLAB simulation software, and the programming language is Python. Data processing and simulation are done in this configuration, ensuring efficient calculations and accurate model training.

Table 1 provides the parameters set in the experiment.

thumbnail
Download:
Table 1. The parameters set in the experiment under two models.

https://doi.org/10.1371/journal.pone.0317277.t001

In addition, this work constructs two flow prediction models: single and dual water levels. The single water level flow prediction model is a single-input and single-output model, where the input is the upstream water level and the output is the channel flow. In contrast, the dual water level flow prediction model has two inputs: the upstream and the downstream cross-sectional water levels, with the output being the channel flow. In the BPNN model, the number of nodes in the hidden layer is set to 6 for the single water level flow prediction model and 12 for the dual water level model. In the EGA-BPNN model, the architecture for the single water level flow prediction model is 1-6-1 (input-hidden-output), and for the dual water level model, it is 2-12-1. The corresponding encoding lengths for these models are 19 and 49, respectively.

4.3 Performance evaluation

4.3.1. Analysis of results for BPNN flow prediction models.

Fig 5 presents partial results of the flow prediction models for the single and dual water levels under the BPNN.

thumbnail
Download:
Fig 5. Partial comparison of flow prediction results between single and dual water level models under the BPNN.

https://doi.org/10.1371/journal.pone.0317277.g005

Fig 5 reveals that the performance of the single water level prediction model is mediocre. While it can generally capture the trend of flow changes, significant errors are present in certain samples, indicating lower prediction accuracy. In contrast, the dual water level prediction model is relatively more accurate, aligning more closely with the actual flow and delivering overall better performance. However, some prediction errors remain in extremely rare samples.

Fig 6 depicts partial RE results for the single and dual water level models under the BPNN.

thumbnail
Download:
Fig 6. Partial RE for flow prediction models of single and dual water levels under the BPNN.

https://doi.org/10.1371/journal.pone.0317277.g006

Fig 6 illustrates that, under the standalone BPNN, the absolute RE values for the single water level flow prediction model range from a minimum of 0.03% to a maximum of 10.8%, with an average of 3.415%. For dual water level flow prediction, the absolute RE values range from a minimum of 0.02% to a maximum of 2.01%, with an average of 1.09%. The smaller overall RE for the dual water level model indicates a relatively accurate prediction of actual flow.

4.3.2. Analysis of flow prediction results for EGA-BPNN models.

Simulation of EGA-BPNN models is conducted using MATLAB software. Fig 7 illustrates partial results for flow prediction models of single and dual water levels.

thumbnail
Download:
Fig 7. Partial comparison of flow prediction results between single and dual water level models with the GA-BP algorithm.

https://doi.org/10.1371/journal.pone.0317277.g007

Fig 7 suggests that in most samples, the prediction results of the single water level model accurately reflect the changing trend of actual flow. The dual water level prediction model exhibits a small RE for all samples, indicating its ability to accurately capture changes in actual flow. Based on Fig 6, it can be concluded that whether using the standalone BPNN or the optimized EGA-BPNN model, the dual water level prediction model demonstrates stabler and more accurate flow prediction performance than the single water level model.

Fig 8 presents the RE for partial prediction results of single and dual water level models using the GA-BP algorithm.

thumbnail
Download:
Fig 8. RE for partial flow prediction results of single and dual water level models based on the GA-BP algorithm.

https://doi.org/10.1371/journal.pone.0317277.g008

Fig 8 shows that under the EGA-BPNN model, the absolute RE for the single water level flow prediction model ranges from a minimum of 0.12% to a maximum of 5.37%, with an average of 1.87%. For dual water level flow prediction, the absolute RE values range from a minimum of 0.03% to a maximum of 1.12%, with an average of 0.41%. Similar to the standalone BPNN model, the overall RE for the dual water level model is smaller under the EGA-BPNN model. It suggests that the optimized EGA-BPNN model provides more accurate predictions of actual flow than the standalone BPNN model.

4.3.3. Comparison of prediction accuracy between BPNN and EGA-BPNN models.

The MSE and MSA values predicted by single and dual water level flow models are compared between the standalone BPNN model and the EGA-BP model optimized by the GA algorithm. Table 2 presents the results.

thumbnail
Download:
Table 2. Comparison of prediction results between BPNN and EGA-BP models.

https://doi.org/10.1371/journal.pone.0317277.t002

Table 2 exhibits that the EGA-BPNN model has smaller MSE and MSA values than the BPNN model in both tasks. The maximum difference between their MSE values is 2.11. Hence, the EGA-BPNN model outperforms the BPNN model in both flow prediction tasks. This suggests that the introduction of GA has a positive impact on enhancing model performance across diverse tasks.

Finally, the performance of EGA-BPNN and Kashyap et al. (2021) [62] models under different soils and crops are compared, and the results are detailed in Table 3.

thumbnail
Download:
Table 3. Comparison of prediction results between two models under different environments and crops.

https://doi.org/10.1371/journal.pone.0317277.t003

Table 3 illustrates that the EGA-BPNN demonstrates a remarkable advantage across various soils and crops. It indicates that the BPNN optimized by EGA has stronger global optimization capabilities, reducing the impact of local optima, and significantly enhancing the model’s accuracy and stability. For the same soil type, differences in crop types affect the model’s prediction performance, primarily because different crops have varying requirements for water and temperature, leading to predicted differences in irrigation needs. On sandy and loamy soils, the prediction accuracy for wheat is relatively high, followed by corn, with soybeans having slightly larger prediction errors. This may be due to the greater impact of soybeans’ water demand and soil adaptability on model predictions. The MSE and MRE for clay soils are generally higher, possibly because such soils have a strong water retention capacity with slower moisture changes. Models need to capture these variations better, thus potentially making them more challenging to predict.

4.3.4. Effect of different hidden layers on model performance.

To evaluate and compare the performance of the EGA-BPNN model with different numbers of hidden layers and parameters, a series of experiments are designed to test the model’s performance under various settings. Specifically, the work compares the influence of the number of hidden layer nodes on model performance and records the corresponding error indicators. The experiments involve training and testing single and dual water level flow prediction models with varying numbers of hidden layer nodes. Table 4 presents the prediction performance of the EGA-BPNN model with different numbers of hidden layer nodes.

thumbnail
Download:
Table 4. Prediction performance of the EGA-BPNN model with different numbers of hidden layer nodes.

https://doi.org/10.1371/journal.pone.0317277.t004

Table 4 shows that as the number of hidden layer nodes increases, the prediction performance of the EGA-BPNN model significantly improves, as reflected in the reduction of MSE and RE. For the single water level flow prediction model, when the number of hidden layer nodes increases from 6 to 16, the MSE decreases from 4.53×10−4 to 3.68×10−4, and the RE drops from 1.87% to 1.29%. Similarly, for the dual water level flow prediction model, increasing the number of hidden layer nodes from 6 to 16 results in a decrease in MSE from 2.38×10−4 to 1.66×10−4, and a reduction in RE from 0.41% to 0.24%. This trend indicates that increasing the number of hidden layer nodes can effectively enhance the prediction accuracy of the EGA-BPNN model. Particularly in the dual water level flow prediction model, the reduction in prediction error is more pronounced, possibly because this model captures more detailed water flow information, thereby improving accuracy. As the number of nodes increases, the model can learn more complex nonlinear relationships, better fitting the training data and reducing prediction error. However, while increasing the number of hidden layer nodes can enhance model performance, the risk of overfitting must be considered. Too many nodes could lead to a model that excels on training data but performs poorly on test data. Therefore, in practical applications, selecting an appropriate number of hidden layer nodes should balance the model’s prediction accuracy and generalization ability to achieve optimal performance. In conclusion, the experiments validate the impact of varying the number of hidden layer nodes on the EGA-BPNN model’s performance. The findings show that increasing the number of nodes can significantly improve prediction performance, but it is also important to balance model complexity and generalization ability.

4.4 Discussion

Additionally, recent research literature across various domains demonstrates the superior prediction performance of composite models, such as the EGA-BPNN. For instance, Lu et al. (2021) proposed a hybrid forecasting method based on ARIMA and LSTM for short-term traffic flow prediction. Their findings revealed that the proposed dynamic weighted combination model outperformed individual models, validating the generality of the approach [63]. Similarly, Wang et al. (2020) introduced the ICPSO-BPNN model, which integrated an improved chaotic particle swarm optimization (ICPSO) with BPNN, for monthly tourism demand predicting. The results indicated that ICPSO-BPNN outperformed standalone BPNN, ARIMA, support vector regression, and other popular existing models [64]. Zhai et al. (2021) used the seasonal trend decomposition analysis of LOESS and lunar data to analyze the seasonal characteristics of human brucellosis in Shanxi Province from 2007 to 2017. They compared the prediction performance of the ARIMA model, a combination model of ARIMA and BPNN (ARIMA-BPNN), and an ARIMA and Elman recurrent neural network (ARIMA-ERNN) combination model. Their results demonstrated that the ARIMA-ERNN model achieved the highest fitting and prediction accuracy, surpassing the ARIMA-BPNN and ARIMA models [65]. In summary, an increasing number of studies suggest that combining neural network models and applying them to predict future industry trends can yield favorable results.

5 Conclusion

5.1 Research contribution

To investigate an AI-based agricultural irrigation warning system, this work focuses on predicting irrigation flow in farmland. The principles and challenges of the BPNN are analyzed, and the network is optimized using the GA algorithm. An EGA-BPNN model is constructed to forecast irrigation flow in farmland. Through a comparative analysis of prediction performance between the EGA-BPNN model and the standalone BPNN model, the following conclusions are drawn:

  1. Whether in the standalone BPNN or the optimized EGA-BPNN model, the dual water level prediction model exhibits stabler and more accurate flow prediction performance than the single water level model.
  2. Under the standalone BPNN model, the absolute mean value of RE for flow prediction is 1.09%. In contrast, the EGA-BPNN model achieves an absolute mean RE value of 0.41% for single flow prediction, indicating that the EGA-BPNN model possesses better prediction performance.
  3. Compared to the BPNN, the EGA-BPNN model shows a decrease of 2.11 in MSE values. Therefore, the EGA-BPNN model performs excellently in predicting irrigation flow in farmland than the BPNN model, further confirming the positive impact of introducing GA on enhancing model performance.
  4. This work explores the impact of the number of hidden layer nodes on model performance. It can be found that appropriately increasing the number of nodes can further improve prediction accuracy while being cautious of the risk of overfitting. The findings enrich the theoretical foundation of smart agriculture and provide strong technical support for agricultural irrigation decision-making, contributing to the precise management of water resources and sustainable agricultural development.

The proposed EGA-BPNN model demonstrates superior performance in agricultural irrigation flow prediction, offering broad practical application prospects, particularly in the fields of smart agriculture and water resource management. In actual agricultural production, irrigation management is a key factor in ensuring crop growth, improving water resource utilization efficiency, and ensuring the sustainable development of agriculture. However, traditional irrigation systems often rely on human experience and fixed rules, making it difficult to respond to environmental changes and dynamically adjust to crop demands. Therefore, AI-based irrigation warning systems, such as the proposed EGA-BPNN model, can accurately predict agricultural irrigation flow based on real-time climate, soil moisture, crop growth status, and various other factors, thereby achieving intelligent scheduling and precise management. In practical applications, the EGA-BPNN model can be integrated into existing smart agriculture systems as an irrigation decision-support tool. By combining with soil moisture sensors, meteorological data collection systems, and crop growth monitoring systems, the model can collect and analyze various environmental variables in real-time to provide accurate predictive data for agricultural irrigation. These data help automatically adjust the start and stop times and flow of irrigation systems, reduce water resource waste, prevent over-irrigation or under-irrigation, and ensure that the growth needs of crops are met. Specifically, the EGA-BPNN model can predict flow based on historical data and real-time information, providing accurate irrigation demand forecasts for agricultural managers. By interfacing with existing intelligent control platforms of irrigation systems, it can achieve automated adjustment of irrigation systems and improve overall water resource utilization efficiency. Furthermore, combined with big data analysis and IoT technology, the EGA-BPNN model can be flexibly applied in diverse agricultural scenarios, offering customized solutions for irrigation management of different regions and crop types.

In summary, applying the EGA-BPNN model not only enhances the intelligent level of irrigation management but also provides a more scientific and precise basis for decision-making in the agricultural field. Thus, it can promote the sustainable management of agricultural water resources and support the further development of smart agriculture.

5.2 Future works and research limitations

Despite the advancements in improving the accuracy of farmland irrigation predictions, this work has some limitations and areas for future improvement. First, the current model is primarily trained and validated on experimental data from a specific region, and its generalization ability and adaptability need further examination under different geographic and climatic conditions. Second, while increasing the number of hidden layer nodes in the model can improve prediction accuracy, too many nodes may lead to increased model complexity, higher computational cost, and a greater risk of overfitting. Therefore, future work could explore more effective model optimization strategies to balance prediction accuracy and generalization ability. Moreover, this work focuses mainly on irrigation flow prediction, and future research could expand to multidimensional agricultural management decision support, such as crop pest and disease prediction and soil fertility assessment. Lastly, with the development of big data and cloud computing technologies, these tools present promising opportunities for constructing and optimizing smart agricultural models. They can effectively handle larger datasets and improve real-time performance and prediction accuracy, making this an important direction for future research. By driving continuous technological innovation and fostering practical applications, this work aims to make meaningful contributions to the advancement of smart agriculture.

References

  1. 1. Sinha B B, Dhanalakshmi R. Recent advancements and challenges of Internet of Things in smart agriculture: A survey. Future Generation Computer Systems, 2022, 126, pp. 169–184.
  2. 2. Li Q, Hu G. Multistage stochastic programming modeling for farmland irrigation management under uncertainty. Plos one, 2020, 15(6), pp. e0233723. pmid:32484821
  3. 3. Zhang Z, Li X, Liu L, et al. Influence of mulched drip irrigation on landscape scale evapotranspiration from farmland in an arid area. Agricultural Water Management, 2020, 230, pp. 105953.
  4. 4. Kumar R, Kumar P, Aljuhani A, et al. Deep learning and smart contract-assisted secure data sharing for IoT-based intelligent agriculture. IEEE Intelligent Systems, 2022, 38(4): 42–51.
  5. 5. Dhanya V G, Subeesh A, Kushwaha N L, et al. Deep learning based computer vision approaches for smart agricultural applications. Artificial Intelligence in Agriculture, 2022, 6: 211–229.
  6. 6. Sharafi L, Zarafshani K, Keshavarz M, et al. Farmers’ decision to use drought early warning system in developing countries. Science of the Total Environment, 2021, 758, pp. 142761. pmid:33183818
  7. 7. Glória A, Cardoso J, Sebastião P. Sustainable irrigation system for farming supported by machine learning and real-time sensor data. Sensors, 2021, 21(9), pp. 3079. pmid:33925142
  8. 8. Jiang Z, Yang S, Liu Z, et al. Coupling machine learning and weather forecast to predict farmland flood disaster: A case study in Yangtze River basin. Environmental Modelling & Software, 2022, 155, pp. 105436.
  9. 9. Kim S N, Jun S M, Lee H J, et al. Establishment of inundation probability DB for forecasting the farmland inundation risk using weather forecast data. Journal of the Korean Society of Agricultural Engineers, 2020, 62(4), pp. 33–43.
  10. 10. Muller C F, Neal M B, Carey-Smith T K, et al. Incorporating weather forecasts into risk-based irrigation decision-making. Australasian Journal of Water Resources, 2021, 25(2), pp. 159–172.
  11. 11. Wright L G, Onodera T, Stein M M, et al. Deep physical neural networks trained with backpropagation. Nature, 2022, 601(7894), pp. 549–555. pmid:35082422
  12. 12. Li B, Shen L, Zhao Y, et al. Quantification of interfacial interaction related with adhesive membrane fouling by genetic algorithm back propagation (GABP) neural network. Journal of Colloid and Interface Science, 2023, 640, pp. 110–120. pmid:36842417
  13. 13. Reza Kashyzadeh K, Amiri N, Ghorbani S, et al. Prediction of concrete compressive strength using a back-propagation neural network optimized by a genetic algorithm and response surface analysis considering the appearance of aggregates and curing conditions. Buildings, 2022, 12(4), pp. 438.
  14. 14. Chen M, Cui Y, Wang X, et al. A reinforcement learning approach to irrigation decision-making for rice using weather forecasts. Agricultural Water Management, 2021, 250, pp. 106838.
  15. 15. Sadeghi Gargari N, Panahi R, Akbari H, et al. Long-Term Traffic Forecast Using Neural Network and Seasonal Autoregressive Integrated Moving Average: Case of a Container Port. Transportation Research Record, 2022, 2676(8), pp. 236–252.
  16. 16. Suresh M. Analyzing and Forecasting of Electricity Consumption by Integration of Autoregressive Integrated Moving Average Model with Neural Network on Smart Meter Data. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2021, 12(11), pp. 1986–1997.
  17. 17. Guo X, Zhu S, Wu J. A hybrid seasonal autoregressive integrated moving average and denoising autoencoder model for atmospheric temperature profile prediction. Big Data, 2022, 10(6), pp. 493–505. pmid:34918943
  18. 18. Hamrani A, Akbarzadeh A, Madramootoo C A. Machine learning for predicting greenhouse gas emissions from agricultural soils. Science of The Total Environment, 2020, 741, pp. 140338. pmid:32610233
  19. 19. Sumathi M, Rajkamal M, Raja S P, et al. A crop yield prediction model based on an improved artificial neural network and yield monitoring using a blockchain technique. International journal of Wavelets, Multiresolution and Information processing, 2022, 20(06), pp. 2250030.
  20. 20. Rashid M, Bari B S, Yusup Y, et al. A comprehensive review of crop yield prediction using machine learning approaches with special emphasis on palm oil yield prediction. IEEE access, 2021, 9, pp. 63406–63439.
  21. 21. Zhang J, Qu S. Optimization of backpropagation neural network under the adaptive genetic algorithm. Complexity, 2021, 2021(1), pp. 1718234.
  22. 22. Chen N, Xiong C, Du W, et al. An improved genetic algorithm coupling a back-propagation neural network model (IEGA-BPNN) for water-level predictions. Water, 2019, 11(9), pp. 1795.
  23. 23. Alfred R. A genetic-based backpropagation neural network for forecasting in time-series data[C]//2015 International Conference on Science in Information Technology (ICSITech). IEEE, 2015, pp. 158–163.
    • 24. Shen X, Zheng Y, Zhang R. A hybrid forecasting model for the velocity of hybrid robotic fish based on back-propagation neural network with genetic algorithm optimization. IEEE Access, 2020, 8, pp. 111731–111741.
    • 25. Xia Z, Peng Y, Lin C, et al. A spatial frequency/spectral indicator-driven model for estimating cultivated land quality using the gradient boosting decision tree and genetic algorithm-back propagation neural network. International Soil and Water Conservation Research, 2022, 10(4), pp. 635–648.
    • 26. Zhao H, Huang F, Li L, et al. Optimization of wastewater anaerobic digestion treatment based on GA-BP neural network. 2018, 122, pp.30–35.
    • 27. Chen J, Liu Z, Yin Z, et al. Predict the effect of meteorological factors on haze using BP neural network. Urban Climate, 2023, 51, pp. 101630.
    • 28. Song S, Xiong X, Wu X, et al. Modeling the SOFC by BP neural network algorithm. International Journal of Hydrogen Energy, 2021, 46(38), pp. 20065–20077.
    • 29. Qin X, Liu Z, Liu Y, et al. User OCEAN personality model construction method using a BP neural network. Electronics, 2022, 11(19), pp. 3022.
    • 30. Tian J, Liu Y, Zheng W, et al. Smog prediction based on the deep belief-BP neural network model (DBN-BP). Urban Climate, 2022, 41, pp. 101078.
    • 31. Zhang X R, Sun X, Sun W, et al. Deformation expression of soft tissue based on BP neural network. Intelligent Automation & Soft Computing, 2022, 32(2), pp. 1041–1053.
    • 32. Han J X, Ma M Y, Wang K. Product modeling design based on genetic algorithm and BP neural network. Neural Computing and Applications, 2021, 33, pp. 4111–4117.
    • 33. Liu P, Zhang W. A fault diagnosis intelligent algorithm based on improved BP neural network. International Journal of Pattern Recognition and Artificial Intelligence, 2019, 33(09), pp. 1959028.
    • 34. Kaveh M, Mesgari M S. Application of meta-heuristic algorithms for training neural networks and deep learning architectures: A comprehensive review. Neural Processing Letters, 2023, 55(4), pp. 4519–4622.
    • 35. Kuck J, Chakraborty S, Tang H, et al. Belief propagation neural networks. Advances in Neural Information Processing Systems, 2020, 33, pp. 667–678.
    • 36. Mohebali B, Tahmassebi A, Meyer-Baese A, et al. Probabilistic neural networks: a brief overview of theory, implementation, and application. Handbook of probabilistic models, 2020, pp. 347–367.
      • 37. Hosseinzadeh M, Ahmed O H, Ghafour M Y, et al. A multiple multilayer perceptron neural network with an adaptive learning algorithm for thyroid disease diagnosis in the internet of medical things. The Journal of Supercomputing, 2021, 77, pp. 3616–3637.
      • 38. Mukherjee A, Jain D K, Goswami P, et al. Back propagation neural network based cluster head identification in MIMO sensor networks for intelligent transportation systems. IEEE Access, 2020, 8, pp. 28524–28532.
      • 39. He S, Sang X, Yin J, et al. Short-term runoff prediction optimization method based on bgru-bp and blstm-bp neural networks. Water Resources Management, 2023, 37(2), pp. 747–768.
      • 40. Song Y, Lei Z, Lu X G, et al. Optimization of a Lobed Mixer with BP Neural Network and Genetic Algorithm. Journal of Thermal Science, 2023, 32(1), pp. 387–400.
      • 41. Mulumba D M, Liu J, Hao J, et al. Application of an Optimized PSO-BP Neural Network to the Assessment and Prediction of Underground Coal Mine Safety Risk Factors. Applied Sciences, 2023, 13(9), pp. 5317.
      • 42. Li X, Wang J, Yang C. Risk prediction in financial management of listed companies based on optimized BP neural network under digital economy. Neural Computing and Applications, 2023, 35(3), pp. 2045–2058.
      • 43. Kashif M, Al-Kuwari S. The impact of cost function globality and locality in hybrid quantum neural networks on NISQ devices. Machine Learning: Science and Technology, 2023, 4(1), pp. 015004.
      • 44. Wang G, Wang J, Wang J, et al. Study on Prediction Model of Soil Nutrient Content Based on Optimized BP Neural Network Model. Communications in Soil Science and Plant Analysis, 2023, 54(4), pp. 463–471.
      • 45. Abdolrasol M G M, Hussain S M S, Ustun T S, et al. Artificial neural networks based optimization techniques: A review. Electronics, 2021, 10(21), pp. 2689.
      • 46. Lyu Z, Yu Y, Samali B, et al. Back-propagation neural network optimized by K-fold cross-validation for prediction of torsional strength of reinforced Concrete beam. Materials, 2022, 15(4), pp. 1477. pmid:35208015
      • 47. Bai H, Cao Q, An S. Mind evolutionary algorithm optimization in the prediction of satellite clock bias using the back propagation neural network. Scientific Reports, 2023, 13(1), pp. 2095. pmid:36747070
      • 48. Katoch S, Chauhan S S, Kumar V. A review on genetic algorithm: past, present, and future. Multimedia tools and applications, 2021, 80, pp. 8091–8126. pmid:33162782
      • 49. Sohail A. Genetic algorithms in the fields of artificial intelligence and data sciences. Annals of Data Science, 2023, 10(4), pp. 1007–1018.
      • 50. Wang Z Z, Sobey A. A comparative review between Genetic Algorithm use in composite optimisation and the state-of-the-art in evolutionary computation. Composite Structures, 2020, 233, pp. 111739.
      • 51. Gad A F. Pygad: An intuitive genetic algorithm python library. Multimedia Tools and Applications, 2023, pp. 1–14.
      • 52. Kim C, Batra R, Chen L, et al. Polymer design using genetic algorithm and machine learning. Computational Materials Science, 2021, 186, pp. 110067.
      • 53. Reddy G T, Reddy M P K, Lakshmanna K, et al. Hybrid genetic algorithm and a fuzzy logic classifier for heart disease diagnosis. Evolutionary Intelligence, 2020, 13, pp. 185–196.
      • 54. Hamdia K M, Zhuang X, Rabczuk T. An efficient optimization approach for designing machine learning models based on genetic algorithm. Neural Computing and Applications, 2021, 33, pp. 1923–1933.
      • 55. Liu B. Review of swarm intelligence algorithm optimization of BP neural network. Academic Journal of Computing & Information Science, 2023, 6(6), pp. 151–155.
      • 56. Jiang M, Pan Z. Optimization of micro-channel heat sink based on genetic algorithm and back propagation neural network. Thermal Science, 2023, 27(1 Part A), pp. 179–193.
      • 57. Wang T, Qi Q, Zhang W, et al. Research on Optimization of Profile Parameters in Screw Compressor Based on BP Neural Network and Genetic Algorithm. Energies, 2023, 16(9), pp. 3632.
      • 58. Chikr Elmezouar Z, Alshahrani F, Almanjahie I M, et al. Scalar-on-Function Relative Error Regression for Weak Dependent Case. Axioms, 2023, 12(7), pp. 613.
      • 59. Nazar S, Yang J, Amin M N, et al. Formulation of estimation models for the compressive strength of concrete mixed with nanosilica and carbon nanotubes. Developments in the Built Environment, 2023, 13, pp. 100113.
      • 60. Sadok W, Lopez J R, Smith K P. Transpiration increases under high‐temperature stress: Potential mechanisms, trade‐offs and prospects for crop resilience in a warming world. Plant, Cell & Environment, 2021, 44(7), pp. 2102–2116.
      • 61. Moore C E, Meacham-Hensold K, Lemonnier P, et al. The effect of increasing temperature on crop photosynthesis: from enzymes to ecosystems. Journal of experimental botany, 2021, 72(8), pp. 2822–2844. pmid:33619527
      • 62. Kashyap P K, Kumar S, Jaiswal A, et al. Towards precision agriculture: IoT-enabled intelligent irrigation systems using deep learning neural network. IEEE Sensors Journal, 2021, 21(16), pp. 17479–17491.
      • 63. Lu S, Zhang Q, Chen G, et al. A combined method for short-term traffic flow prediction based on recurrent neural network. Alexandria Engineering Journal, 2021, 60(1), pp. 87–94.
      • 64. Wang L, Wu B, Zhu Q, et al. Forecasting monthly tourism demand using enhanced backpropagation neural network. Neural Processing Letters, 2020, 52, pp. 2607–2636.
      • 65. Zhai M, Li W, Tie P, et al. Research on the predictive effect of a combined model of ARIMA and neural networks on human brucellosis in Shanxi Province, China, pp. a time series predictive analysis. BMC Infectious Diseases, 2021, 21(1), pp. 1–12.