Fitting of Nonlinear Function Based on Elman Neural Network

In order to estimate daily solar radiation, this paper proposes Elman (ENN) and Feed forward backpropagation (FNN) neural networks. The time series data from the location of Kenitra City, Morocco is used to train the created models. Fletcher-Powell Conjugate Gradient (CGF), Scaled Conjugate Gradient (SCG), Resilient Backpropagation (RB), Conjugate gradient with Powell-Beale restarts (CGB), Levenberg-Marquardt (LM), Polak-Ribi´ere Conjugate Gradient (CGP), and One Step Secant (OSS) are also used with both, the ENN and FNN to identify the best and effective training function for each. The models with various training algorithms are tested by using evaluation metrics root mean square error (RMSE), mean square error (MSE) and mean absolute error (MAE). The study showed that the Elman Neural Network had an excellent daily solar radiation prediction for Kenitra city. Good results have been obtained with Levenberg-Marquardt algorithm.

Short-term power load forecasting based on Elman neural network with particle swarm optimization

Gross domestic product (GDP) can well reflect the development of the economy, and predicting GDP can help better grasp the future economic trends. In this article, three different neural network models, the genetic algorithm – back-propagation neural network model, the particle swarm optimization (PSO) – Elman neural network (Elman NN) model, and the bat algorithm – long short-term memory model, were analyzed based on neural networks. The GDP data of Sichuan province from 1992 to 2020 were collected to compare the performance of the three models in predicting GDP. It was found that the mean absolute percentage error values of the three models were 0.0578, 0.0236, and 0.0654, respectively; the root-mean-square error values were 0.0287, 0.0166, and 0.0465, respectively; and the PSO-Elman NN model had the best performance in GDP prediction. The experimental results demonstrate that neural networks were reliable in predicting GDP and can be used for further applications in practice.

Knowledge base operator support system for nuclear power plant fault diagnosis

Accurate estimation of the state of charge (SOC) of lithium batteries is the research hotspot. As a dynamic recurrent neural network, Elman neural network has a simple structure and can adapt to time-varying characteristics, which have led to its widespread application in the field of SOC prediction. However, the simple network structure can also cause problems such as low learning efficiency, easy to fall into local extremes, and difficulty converge to the optimal weight solution. This paper proposes to combine the whale optimization algorithm (WOA) with genetic algorithm (GA) to optimize the weights and thresholds of the Elman neural network, thus improving the learning speed and prediction accuracy. We select three parameters of current, voltage and temperature as system variables, and simulate the experimental data. The experimental results show that, compared with the traditional Elman neural network and the Elman neural network optimized only by genetic algorithm, the hybrid algorithm performs best. The number of network iterations is small, and the average error drops below 1%.

The Sixth International Symposium on Neural Networks (ISNN 2009)

Fuzzy PID controller is difficult in implementation for its computational complexity. In this paper, for the dynamic modeling and parallel computation ability of Elman NN (Neural Network), the authors utilized an equivalent Elman NN to accurately approximate the dynamics of a known fuzzy PID controller. Consequently, the same process model was controlled by the fuzzy PID controller and the remodeling Elman NN, respectively. The results show that the control qualities of two different controllers were extremely similar. Thus, the fuzzy PID controller can be simplified to a remodeling Elman NN in purpose of reducing the computational complexity, solving the curse of dimensionality and improving the real-time performance.

The electric power industry is closely related to the development of national economy. With the development of economy, the social electricity situation is increasingly complicated, which brings great test to the prediction of electric load system. Accurate short-term power load forecasting plays an important role in production scheduling and safe and stable operation of power system. In this paper, Elman neural network based on genetic algorithm is established and a short-term power load forecasting model is established. The actual history data of municipal power grid are simulated, the experimental results show that compared with the BP neural network and Elman neural network commonly, Elman neural network based on genetic algorithm to solve the problem of random initial weights of the Elman neural network, can effectively enhance the power load forecasting accuracy and meet the needs of the actual production and work.

This paper presents an approach of position sensorless control for permanent magnet linear synchronous motors (PMLSM) based on Elman neural network. The Elman neural network observer can be considered as a special kind of feed-forward neural network with additional memory neurons and local feedback. Because of the context neurons and local recurrent connections between the context layer and the hidden layer, it facilitates the nonlinear states estimation for the sensorless control of PMLSM. The Elman neural network is trained both off-line and on-line. In the off-line training process with the training data, the connective weights of the Elman neural network are trained by the Levenberg-Marquardt algorithm, while on-line learning, the connective weights of the Elman neural network are trained using supervised gradient decent method. The effectiveness of the proposed observer is confirmed by the digital simulations results.

There is a function of dynamic mapping when processing non-linear complex data with Elman neural networks. Because Elman neural network inherits the feature of back-propagation neural network to some extent, it has many defects; for example, it is easy to fall into local minimum, the fixed learning rate, the uncertain number of hidden layer neuron and so on. It affects the processing accuracy. So we optimize the weights, thresholds and numbers of hidden layer neurons of Elman networks by genetic algorithm. It improves training speed and generalization ability of Elman neural networks to get the optimal algorithm model. It has been proved by instance analysis that new algorithm was superior to the traditional model in terms of convergence rate, predicted value error, number of trainings conducted successfully, etc. It indicates the effect of the new algorithm and deserves further popularization.

Keywords: Time series estimation, Flow Estimation, Elman Neural Networks Abstract: This paper investigates the application of partially recurrent artificial neural networks (ANN) in the flow estimation for Sao Francisco River that feeds the hydroelectric power plant of Sobradinho. An Elman neural network was used suitably arranged to receive samples of the flow time series data available for Sao Francisco River shifted by one month. For that, the neural network input had a delay loop that included several sets of inputs separated in periods of five years monthly shifted. The considered neural network had three hidden layers. There is a feedback between the output and the input of the first hidden layer that enables the neural network to present temporal capabilities useful in tracking time variations. The data used in the application concern to the measured Sao Francisco river flow time series from 1931 to 1996, in a total of 65 years from what 60 were used for training and 5 for testing. The obtained results indicate that the Elman neural network is suitable to estimate the river flow for 5 year periods monthly. The average estimation error was less than 0.2 %

The quantification of the relationship between morphological and color indicators in various organs of horticultural crops is of great significance for crop digital visualization research using computer vision technology. To study this relationship, observational data from a six-year experiment were collected, focusing on seven kinds of color component values of different organs including root, stem, and leaf. Using the collected color data as input, a simulation model was established based on the Elman neural network for six horticultural crops including zizania, cucumber, celery, spinach, parsley, and tea. Results indicated that the horticultural crop morphology model based on the Elman neural network exhibited high simulation accuracy with root mean square error (RMSE) ranging from 0.14 to 1.05 cm and normalized root mean square error (NRMSE) ranging from 2.02% to 11.34% for the maximum root length simulation model. The simulation model for stem length and diameter had an RMSE ranging from 1.42 to 4.96 cm and 0.25 to 1.17 mm, respectively, with NRMSE ranging from 18.19% to 25.65% and 15.13% to 27.25%, respectively. Similarly, chlorophyll content, leaf length, leaf width, and leaf area simulation models exhibited RMSE ranging from 2.80 to 8.22 SPAD, 0.44 to 18.04 cm, 0.22 to 3.49 cm, and 0.25 to 36.39 cm2, respectively, with NRMSE ranging from 8.63% to 21.04%, 15.00% to 22.87%, 15.12% to 33.58%, and 6.88% to 24.90%, respectively. These findings provide essential theoretical support for precision agriculture in areas of water and fertilizer management, plant growth diagnosis, and yield prediction. Keywords: horticultural crop, morphology, color, Elman neural network, root, stem and leaf DOI: 10.25165/j.ijabe.20251805.8435 Citation: Cheng C, Lyu Y, Feng L P, Qin H X, Che X Q, Chen S N, et al. Retrieval of horticultural crop morphology from color based on Elman neural network. Int J Agric & Biol Eng, 2025; 18(5): 259–267.

Solar irradiation is the most critical parameter to consider when designing solar energy systems. The high cost and difficulty of measuring solar irradiation makes it impractical in every location. This study’s primary objective was to develop an artificial neural network (ANN) model for global horizontal irradiation (GHI) prediction using satellite data inputs. Three types of ANN, namely, the feed forward neural network (FFNN), cascaded forward neural network (CFNN), and Elman neural network (EMNN), were tested. The findings revealed that altitude, relative humidity, and satellite GHI are the most effective parameters, as they are present in all the best-performing models. The best model for daily GHI prediction was FFNN, which decreased daily MAPE, RMSE, and MBE by 25.4%, 0.11 kWh/m2/d, and 0.01 kWh/m2/d. The FFNN daily MAPE, RMSE, and MBE values were 7.83%, 0.49 kWh/m2/d, and 0.01 kWh/m2/d. The EMNN performed best for monthly and annual prediction, reducing monthly MAPE, RMSE, and MBE by 50.62%, 0.13 kWh/m2/d, and 0.13 kWh/m2/d, while the reduction for yearly was 91.6%, 0.11 kWh/m2/d, 0.2 kWh/m2/d. The EMNN monthly MAPE, RMSE, and MBE values were 3.36%, 0.16 kWh/m2/d, and 0.16 kWh/m2/d, while the yearly values were 0.47%, 0.18 kWh/m2/d, and 0.004 kWh/m2/d.

High-dimensional large sample data sets, between feature variables and between samples, may cause some correlative or repetitive factors, occupy lots of storage space, and consume much computing time. Using the Elman neural network to deal with them, too many inputs will influence the operating efficiency and recognition accuracy; too many simultaneous training samples, as well as being not able to get precise neural network model, also restrict the recognition accuracy. Aiming at these series of problems, we introduce the partial least squares (PLS) and cluster analysis (CA) into Elman neural network algorithm, by the PLS for dimension reduction which can eliminate the correlative and repetitive factors of the features. Using CA eliminates the correlative and repetitive factors of the sample. If some subclass becomes small sample, with high-dimensional feature and fewer numbers, PLS shows a unique advantage. Each subclass is regarded as one training sample to train the different precise neural network models. Then simulation samples are discriminated and classified into different subclasses, using the corresponding neural network to recognize it. An optimized Elman neural network classification algorithm based on PLS and CA (PLS-CA-Elman algorithm) is established. The new algorithm aims at improving the operating efficiency and recognition accuracy. By the case analysis, the new algorithm has unique superiority, worthy of further promotion.

A greenhouse control with feed-forward and recurrent neural networks