A Weighted EFOR Algorithm for Dynamic Parametrical Model Identification of the Nonlinear System

In this paper, the Nonlinear Auto-Regressive with exogenous inputs (NARX) model with parameters of interest for design (NARX-M-for-D), where the design parameter of the system is connected to the coefficients of the NARX model by a predefined polynomial function is studied. For the NARX-M-for-D of nonlinear systems, in practice, to predict the output by design parameter values are often difficult due to the uncertain relationship between the design parameter and the coefficients of the NARX model. To solve this issue and conduct the analysis and design, an improved algorithm, defined as the Weighted Extended Forward Orthogonal Regression (WEFOR), is proposed. Firstly, the initial NARX-M-for-D is obtained through the traditional Extended Forward Orthogonal Regression (EFOR) algorithm. Then a weight matrix is introduced to modify the polynomial functions with respect to the design parameter, and then an improved model, which is referred to as the final NARX-M-for-D is established. The genetic algorithm (GA) is used for deriving the weight matrix by minimizing the normalized mean square error (NMSE) over the data sets corresponding to the design parameter values used for modeling and first prediction. Finally, both the numerical and experimental studies are conducted to demonstrate the application of the WEFOR algorithm. The results indicate that the final NARX-M-for-D can accurately predict the system output of a nonlinear system. The new algorithm is expected to provide a reliable model for dynamic analysis and design of the nonlinear system.

A data calibration method for micro air quality detectors based on a LASSO regression and NARX neural network combined model

Studies have shown that there is a certain correlation between air pollution and various human diseases, especially lung diseases, so it is very meaningful to monitor the concentration of pollutants in the air. Compared with the national air quality monitoring station (national control point), the micro air quality detector has the advantage that it can monitor the concentration of pollutants in real time and grid, but its measurement accuracy needs to be improved. This paper proposes a model combining the least absolute selection and shrinkage operator (LASSO) regression and nonlinear autoregressive models with exogenous inputs (NARX) to calibrate the data measured by the micro air quality detector. Before establishing the LASSO-NARX model, correlation analysis is used to test whether the correlation between the concentration of air pollutants and its influencing factors is significant, and to find out the main factors that affect the concentration of pollutants. Due to the multicollinearity between various influencing factors, LASSO regression is used to further screen the influencing factors and give the quantitative relationship between the pollutant concentration and various influencing factors. In order to improve the prediction accuracy of pollutant concentration, the predicted value of each pollutant concentration in the LASSO regression model and the measurement data of the micro air quality detector are used as input variables, and the LASSO-NARX model is constructed using the NARX neural network. Several indicators such as goodness of fit, root mean square error, mean absolute error and relative mean absolute percent error are used to compare various air quality models. The results show that the prediction results of the LASSO-NARX model are not only better than the LASSO model alone and the NARX model alone, but also better than the commonly used multilayer perceptron and radial basis function neural network. Using this model to calibrate the measurement data of the micro air quality detector can increase the accuracy by 61.3–91.7%.

A Data Calibration Method of Micro Air Quality Detector Based on LASSO Regression and NARX Neural Network Combined Model

Studies have shown that there is a certain correlation between air pollution and various human diseases, especially lung diseases, so it is very meaningful to monitor the concentration of pollutants in the air. Compared with the national air quality monitoring station (national control point), the micro air quality detector has the advantage that it can monitor the concentration of pollutants in real time and grid, but its measurement accuracy needs to be improved. In this paper, the measurement data of the micro air quality detector is calibrated with the help of the LASSO regression and NARX neural network combination (LASSO-NARX) model using the data measured by the national control point. First, correlation analysis is used to test whether the correlation between the concentration of air pollutants and its influencing factors is significant. Second, LASSO regression is used to give the quantitative relationship between pollutant concentration and various influencing factors. Third, the predicted value of each pollutant concentration in the LASSO regression model and the measurement data of the micro air quality detector are used as input variables, and the LASSO-NARX model is constructed using the NARX neural network. Finally, several indicators such as Root Mean Square Error, goodness of fit, Mean Absolute Error and Relative Mean Absolute Percent Error are used to compare various air quality models. The results show that the prediction results of the LASSO-NARX model are not only better than the LASSO model alone and the NARX model alone, but also better than the commonly used multilayer perceptron and radial basis function neural network. The LASSO-NARX model performed equally well on the training set and test set, indicating that the model has excellent generalization capabilities. Using this model to calibrate the measurement data of the micro air quality detector can increase the accuracy by 61.3% to 91.7%.

Short-term forecasting of monthly water consumption in hyper-arid climate using recurrent neural networks

Freshwater supply is a major challenge in regions with limited water resources and extremely arid climatic conditions. The objective of this study is to model the monthly water demand in Kuwait using the nonlinear autoregressive with exogenous input (NARX) neural network approach. The country lacks conventional surface water resources and is characterized by extremely arid climate. In addition, it has one of the fastest growing populations. In this study, linear detrending is performed on the water consumption time series for the period from January 1993 to December 2018 to eliminate the influence of population growth before application to the NARX model. Monthly temperature data are selected as exogenous input to the NARX model, because they are strongly associated with the water consumption data. Correlation analyses are performed to determine the input and feedback delays of the NARX model. The results demonstrate that the recurrent NARX model is efficient and robust for forecasting the short-term water demand, with a Nash-Sutcliffe (NS) coefficient of 0.837 in the validation period. Seasonal model assessment shows that the model performs best during the critical summer season. The NARX-based recurrent model is established as a powerful and promising tool for predicting urban water demand. Thus, it can efficiently aid the development of resilient water supply plans.

Forecasting of Photovoltaic Power by Means of Non-Linear Auto-Regressive Exogenous Artificial Neural Network and Time Series Analysis

In this research paper, a nonlinear autoregressive with exogenous input (NARX) model of the nonlinear system based on neural network and time series analysis is proposed to deal with the one-month forecast of the produced power from photovoltaic modules (PVM). The PVM is a monocrystalline cell with a rated production of 175 watts that is placed at Heliopolis University, Bilbéis city, Egypt. The NARX model is considered powerful enough to emulate the nonlinear dynamic state-space model. It is extensively performed to resolve a variety of problems and is mainly important in complex process control. Moreover, the NARX method is selected because of its quick learning and completion times, as well as high appropriateness, and is distinguished by advantageous dynamics and interference resistance. The neural network (NN) is trained and optimized with three algorithms, the Levenberg–Marquardt Algorithm (NARX-LMA), the Bayesian Regularization Algorithm (NARX-BRA) and the Scaled Conjugate Gradient Algorithm (NARX-SCGA), to attain the best performance. The forecasted results using the NARX method based on the three algorithms are compared with experimentally measured data. The NARX-LMA, NARX-BRA and NARX-SCGA models are validated using statistical criteria. In general, weather conditions have a significant impact on the execution and quality of the results.

Machine Learning modeling techniques for forecasting the trophic level in a restored South Mediterranean lagoon using Chlorophyll-α

An Artificial Neural Network (ANN), a Machine Learning (ML) modeling approach is proposed to predict the ecological state of the North Lagoon of Tunis, a shallow restored Mediterranean coastal ecosystem. A Nonlinear Auto Regressive with exogenous input (NARX) neural network model was fitted to predict Chlorophyll- a (Chl- a ) concentrations in the North Lagoon of Tunis as an eutrophication indicator. The modeling is based on approximately three decades of monitoring water quality data (from January 1989 to April 2018) to train, validate and test the NARX model. The most relevant predictor variables used in this model were those having a high permutation importance ranking with Random Forest (RF) model, which simplified the structure of the network, resulting in a more accurate and efficient procedure. Those predictor variables are secchi depth, and dissolved oxygen. Various model scenarios with different NARX architectures were tested for Chl- a prediction. To verify the model performances, the trained models were applied to field monitoring data. Results indicated that the developed NARX model can predict Chl- a concentrations in the North Lagoon of Tunis with high accuracy (R= 0.79; MSE= 0.31). In addition, results showed that the NARX model generally performed better than multivariate linear regression (MVLR). This approach could provide a quick assessment of Chl- a variations for lagoon management and eco-restoration.