Novel Nonlinear Autoregression with External Input Integrating PCA-WD and Its Application to a Dynamic Soft Sensor

Abstract

Important process or product quality parameters in chemical plants are difficult to measure with sensors for economic or technical reasons and soft measurement is an important solution to measure these key parameters. Aiming at the strong nonlinearity, low prediction accuracy, frequent dynamic changes, and severe collinear interference in actual chemical production processes, this article proposes a dynamic soft sensor model using novel nonlinear autoregression with external input (NARX) based on principal component analysis (PCA) and wavelet denoising (WD) (PCA-WD-NARX). The feature information of the sample data is extracted by the PCA and the collinearity is eliminated at the same time. Moreover, the noise in the data set is eliminated by WD to simplify the complexity of the learning data. Then, the NARX is used to construct the dynamic soft sensor model. Finally, the recommended model is applied to predict the acetic acid content of a purified terephthalic acid (PTA) plant. Through the evaluation indexes of the root-mean-square error (RMSE) and the coefficient of determination (R 2), the experimental results show that the proposed method has the most outstanding prediction accuracy and generalization ability among the NARX model, the NARX integrating the PCA (PCA-NARX) model, the NARX integrating the WD (WD-NARX) model, the Elman model, and the recursive radial basis function (RRBF).

Novel Gray Orthogonal Echo State Network Integrating the Process Mechanism for Dynamic Soft Sensor Development

“…Five evaluation indicators including average absolute error (MAE), average percentage error (MAPE), root mean square error (RMSE), average relative error (ARE), and determination coefficient ( R 2 ) are used to evaluate the prediction effect in this paper. , T test denotes the sample number of the testing set. The prediction result based on the proposed algorithm is P = ( p [1],..., p [ T test ]), and the teacher signal in the test set is Y = ( y [1],..., y [ T test ]).…”

“…The RNN has been widely used in the soft sensor model due to its feedback structure having the memory function and the ability of capturing the dynamic characteristics of objects. 24 Zhang et al 9 employed the PCA-WD-NARX algorithm to realize the dynamic soft sensor model of a complex chemical process in purified terephthalic acid plants and achieved remarkable results. However, NARX, which adopts a hierarchical connection structure and is trained by the gradient descent method, still belongs to the traditional RNN and has the risk of gradient explosion and gradient dispersion.…”

“…The influence factors of random error including the measurement delay of various materials, micro change of the electromagnetic field, influence of environmental vibration factors, clearance of measuring instrument parts, and friction are more complex, which lead to the generation of random error. In this paper, WD with the adaptive threshold processing method 9 is used to remove the high-frequency noise of the collected data, of which the wavelet basis function is selected as sym3 and the decomposition level is set to 3. The connection of neurons in the reservoir of the traditional ESN is random and has the problem of approximate collinearity, which may lead to the ill-posed matrix in the training process and the degradation of the model performance.…”

“…Finally, an improved orthogonal sparse ESN is used to construct the dynamic soft sensor model of the PP production process. The comparison with the OESN and other typical dynamic soft sensor models including recursive radial basis function (RRBF) and nonlinear autoregressive with external input (NARX) 9 shows the excellent prediction performance and good generalization ability of the proposed method.…”

Novel Deep Learning Based on Data Fusion Integrating Correlation Analysis for Soft Sensor Modeling

“…Results and Comparison of the Soft SensorModel. The experiment data are divided into training sets and testing sets,44 including 1780 and 40 data, respectively. The AE, the RMSE, and the MAPE are chosen as error indexes to…”