Dynamic Nonlinear Partial Least Squares Modeling Using Gaussian Process Regression

Nonlinear dynamic transfer partial least squares for domain adaptive regression

Aiming to address soft sensing model degradation under changing working conditions, and to accommodate dynamic, nonlinear, and multimodal data characteristics, this paper proposes a nonlinear dynamic transfer soft sensor algorithm. The approach leverages time-delay data augmentation to capture dynamics and projects the augmented data into a latent space for constructing a nonlinear regression model. Two regular terms, distribution alignment regularity and first-order difference regularity, are introduced during data projection to address data distribution disparities. Laplace regularity is incorporated into the nonlinear regression model to ensure geometric structure preservation. The final optimization objective is formulated within the framework of partial least squares, and hyperparameters are determined using Bayesian optimization. The effectiveness of the proposed algorithm is demonstrated through experiments on three public datasets.

Virtual sensing for dynamic industrial process based on localized linear dynamical system models with time-delay optimization

Virtual sensors play an important role in real-time sensing of key quality-related variables in industrial processes. Linear dynamical system (LDS) paradigm has established itself as a powerful tool for developing dynamic virtual sensors. However, there are still some practically pivotal issues unresolved, such as how to improve the generalization reliability and accuracy when accounting for the time delays and how to broaden the application sphere by breaking their limitations to linear processes. Motivated by dealing with these challenging issues this paper proposes a virtual sensing framework called 'localized LDS (LoLDS)'. In the LoLDS framework, the process dynamics and nonlinearities are taken into consideration from different scales without increasing the model complexity, and the time delays are intelligently optimized which triggers the model inconsistency by a designed diversified localization scheme at the offline stage. Moreover, an adaptive online model switch scheme is developed to enable the real-timely best LDS models to be responsible to predict the quality variables. The offline and online operations together enable the LoLDS to improve the generalization performance of the dynamic virtual sensor. The LoLDS framework is highly automated, and its performance has been extensively evaluated by two real-life industrial processes, showing very promising application foregrounds.

Semi-supervised echo state network with temporal-spatial graph regularization for dynamic soft sensor modeling of industrial processes

Echo state network (ESN) has been successfully applied to industrial soft sensor field because of its strong nonlinear and dynamic modeling capability. Nevertheless, the traditional ESN is intrinsically a supervised learning technique, which only depends on labeled samples, but omits a large number of unlabeled samples. In order to eliminate this limitation, this work proposes a semi-supervised ESN method assisted by a temporal-spatial graph regularization (TSG-SSESN) for constructing soft sensor model with all the available samples. Firstly, the traditional supervised ESN is enhanced to construct the semi-supervised ESN (SSESN) model by integrating both unlabeled and labeled samples in the reservoir computing procedure. The SSESN computes the reservoir states under high sampling rate for better process dynamic information mining. Furthermore, the SSESN's output optimization objective is modified by applying the local adjacency graph of all training samples as a regularization term. Especially, in view of the dynamic data characteristic, a temporal-spatial graph is constructed by considering both the temporal relationship and the spatial distances. The applications to a debutanizer column process and a wastewater treatment plant demonstrate that the TSG-SSESN model can build much smoother model and has better generalization capability than the basic ESN models in terms of soft sensor prediction results.

Neural Component Analysis for Key Performance Indicator Monitoring

The partial least squares (PLS) algorithm is a commonly used key performance indicator (KPI)-related performance monitoring method. To address nonlinear features in the process, this paper proposes neural component analysis (NCA)-PLS, which combines PLS with NCA. (NCA)-PLS realizes all the principles of PLS by introducing a new loss function and a new principal component selection mechanism to NCA. Then, the gradient descent formulas for network training are rederived. NCA-PLS can extract components with large correlations with KPI variables and adopt them for data reconstruction. Simulation tests using a mathematical model and the Tennessee Eastman process show that NCA-PLS can successfully handle nonlinear relationships in process data and that it performs much better than PLS, KPLS, and NCA.

Neighborhood component analysis for modeling papermaking wastewater treatment processes

It is of great importance to obtain accurate effluent quality indices in time for pulping and papermaking wastewater treatment processes. However, considering the complex characteristics of industrial wastewater treatment systems, conventional modeling methods such as partial least squares (PLS) and artificial neural networks (ANN) cannot achieve satisfactory prediction accuracy. As a supervised metric learning method, neighborhood component analysis (NCA) is able to significantly improve the prediction performance by training an appropriate model in metric space using the distance between samples for papermaking wastewater treatment processes. The results on two data sets show that NCA has a higher prediction accuracy compared with PLS and ANN. Specifically, NCA has the highest determination coefficient (R²) and the lowest root mean square error in a benchmark simulation data set. On the other hand, the results on the data from an industrial wastewater process indicate that NCA has better modeling accuracy and its R² increases by 32.80% and 29.08% compared with PLS and ANN, respectively. NCA provides a feasible way to realize online monitoring and automatic control in wastewater treatment processes.

A Soft Sensor Approach Based on an Echo State Network Optimized by Improved Genetic Algorithm

In the process of fault diagnosis and the health and safety operation evaluation of modern industrial processes, it is crucial to measure important state variables, which cannot be directly detected due to limitations of economy, technology, environment and space. Therefore, this paper proposes a data-driven soft sensor approach based on an echo state network (ESN) optimized by an improved genetic algorithm (IGA). Firstly, with an ESN, a data-driven model (DDM) between secondary variables and dominant variables is established. Secondly, in order to improve the prediction performance, the IGA is utilized to optimize the parameters of the ESN. Then, the immigration strategy is introduced and the crossover and mutation operators are changed adaptively to improve the convergence speed of the algorithm and address the problem that the algorithm falls into the local optimum. Finally, a soft sensor model of an ESN optimized by an IGA is established (IGA-ESN), and the advantages and performance of the proposed method are verified by estimating the alumina concentration in an aluminum reduction cell. The experimental results illustrated that the proposed method is efficient, and the error was significantly reduced compared with the traditional algorithm.

Multi-grained cascade forest for effluent quality prediction of papermaking wastewater treatment processes

The real time estimation of effluent indices of papermaking wastewater is vital to environmental conservation. Ensemble methods have significant advantages over conventional single models in terms of prediction accuracy. As an ensemble method, multi-grained cascade forest (gcForest) is implemented for the prediction of wastewater indices. Compared with the conventional modeling methods including partial least squares, support vector regression, and artificial neural networks, the gcForest model shows prediction superiority for effluent suspended solid (SS_eff) and effluent chemical oxygen demand (COD_eff). In terms of SS_eff, gcForest achieves the highest correlation coefficient with a value of 0.86 and the lowest root-mean-square error (RMSE) value of 0.41. In comparison with the conventional models, the RMSE value using gcForest is reduced by approximately 46.05% to 50.60%. In terms of COD_eff, gcForest achieves the highest correlation coefficient with a value of 0.83 and the lowest root-mean-square error value of 4.05. In comparison with the conventional models, the RMSE value using gcForest is reduced by approximately 10.60% to 18.51%.