Soft Sensor Model Derived from Wiener Model Structure: Modeling and Identification

Stochastic configuration broad learning system (SCBLS) has demonstrated notable advantages in industrial soft sensing due to its computational efficiency and supervised node configuration. However, conventional SCBLS overlooks the dynamic characteristics of industrial data, which limits the prediction accuracy of soft sensor models. To address this limitation, this study proposes a two‐layer temporal SCBLS (TT‐SCBLS) for industrial soft sensor modelling. The proposed framework consists of two key modules: an output‐related dual‐layer temporal feature extraction module and an enhancement node stochastic configuration module. The former is used to build the primary mapped features, where the first layer employs quality‐related slow feature analysis (QSFA) to extract intrinsic slow features, mitigating the impact of data noise, and the second layer utilizes a cycle reservoir with regular jumps (CRJ) network to capture temporal dependencies in the process data. The later introduces the stochastic configuration algorithm for incremental node expansion at the enhancement layer, ensuring efficient model adaptation. Additionally, a kernel Shapley additive explanation (SHAP) model is integrated to quantify the contributions of input variables, enhancing model transparency. The proposed method is validated on two benchmark industrial systems, with experimental results confirming its superior prediction performance compared to existing approaches.

In recent years, deep learning has been applied to build soft sensor models. Compared to the classical latent variable models, the model based on deep learning has a good performance in tackling nonlinearity in process data. However, static soft sensor based on deep neural network (SSSDNN) fails to take into account the dynamic characteristics, which are unavoidable in some applications. To improve the performance of the soft sensor, a novel dynamic soft sensor model based on impulse response template and deep neural network (DSSDNN) is proposed by means of Wiener structure, and an iterative algorithm will be used to train this novel model. A case study based on real debutanizer column data demonstrates the desirable prediction performance of DSSDNN and shows that the DSSDNN is able to obtain better approximation accuracy than the static soft sensor model in nonlinear processes with dynamic characteristics.

Aiming at the characteristics of soft sensors, an ensemble learning algorithm AdaBoost.RT is used to establish the soft sensor models. According to the shortcoming of AdaBoost.RT and the difficulties of on-line updating for soft sensor models, a self-adaptive modifying threshold φ and an incremental learning method are proposed for improving the performance of original AdaBoost.RT. The new modified AdaBoost.RT can overcome the disadvantages of original AdaBoost.RT and update the soft sensor model in real time. The new method is used to establish the soft sensor model of molten steel temperature in 300t LF. Practical production data are used to test the model. The results demonstrate that the new soft sensor model based on modified AdaBoost.RT can improve the prediction accuracy and has good ability of update.

Batch processes are time-varying, high-dimensional, and highly nonlinear. Some primary variables are difficult to be measured online in real-time. Soft sensor modeling plays a critical role in estimating the primary variables of batch processes. However, the existing methods do not consider the influence of the parameter number, the sample number, and the structure on model performance, which makes it difficult for soft sensors to satisfy the prediction accuracy and stability. To address this issue, a hybrid modeling method based on risk assessment is proposed. Bayesian information criterion and the principle of structural risk minimization are used to evaluate the model risk and calculate the weight of mechanism models and data-driven models. Then, the hybrid models of batch processes are constructed. Experimental results show that the hybrid model based on risk assessment has high prediction accuracy and strong robustness.KeywordsBatch processesSoft sensorRisk assessmentHybrid model

With massive data of a fermentation process, a single data-based soft-sensor modeling method suffers from heavy features and bad accuracy. A novel soft sensor using multi-model neural network (MNN) based on modified kernel fuzzy clustering is proposed. Firstly, Features of sample data are extracted using principal component analysis (PCA) and the secondary variables are determined by PCA. Secondly, a kernel fuzzy c-means clustering algorithm based on particle swarm optimization (PSO) is applied to group the principal data into overlapping clusters, and neural network (NN) is used to construct sub-models based on the clusters. Finally, the estimation of every sub-model is fused by computing the weighted sum of the local models. The proposed modeling method is used to construct a novel soft sensor model for an erythromycin fermentation process. Case studies show that the approach has better performance compared to the conventional single model.

Due to the time lag, nonlinearity, and variable coupling in the process sector, production variables are hard to measure directly and require accurate soft sensor models. In light of this, this research proposes a soft sensor convolution neural network fast recurrent unit (CNN-FRU) network model. Convolution is used to get spatial features and get rid of redundancy data in variables. FRU changes the linear coupling constraint within a gated recurrent unit (GRU) and solves the problem of blocked information flow in GRU. It can be used to extract time-varying delay characteristics from complex processes industry data. FRU is compared with GRU and long short-term memory (LSTM) on a standard dataset to demonstrate the advantages of FRU in terms of training speed and accuracy. As a specific application in the process industry, the proposed soft sensor model is trained and validated on the cement-specific surface area dataset. The experimental results demonstrate that the soft sensor model can be generalized better.

Soft sensor model development in multiphase/multimode processes based on Gaussian mixture regression

This paper introduces a novel soft sensor modeling method based on BDA-IPSO-LSSVM designed to address the issue of model failure caused by varying fermentation data distributions resulting from different operating conditions during the fermentation of different batches of Pichia pastoris. First, the problem of significant differences in data distribution among different batches of the fermentation process is addressed by adopting the balanced distribution adaptation (BDA) method from transfer learning. This method reduces the data distribution differences among batches of the fermentation process, while the fuzzy set concept is employed to improve the BDA method by transforming the classification problem into a regression prediction problem for the fermentation process. Second, the soft sensor model for the fermentation process is developed using the least squares support vector machine (LSSVM). The model parameters are optimized by an improved particle swarm optimization (IPSO) algorithm based on individual differences. Finally, the data obtained from the Pichia pastoris fermentation experiment are used for simulation, and the developed soft sensor model is applied to predict the cell concentration and product concentration during the fermentation process of Pichia pastoris. Simulation results demonstrate that the IPSO algorithm has good convergence performance and optimization performance compared with other algorithms. The improved BDA algorithm can make the soft sensor model adapt to different operating conditions, and the proposed soft sensor method outperforms existing methods, exhibiting higher prediction accuracy and the ability to accurately predict the fermentation process of Pichia pastoris under different operating conditions.

Soft sensors are mathematical models that estimate the value of a process variable that is difficult or expensive to measure directly. They can be based on first principle models, data-based models, or a combination of both. These models are increasingly used in mineral processing to estimate and optimize important performance parameters such as mill load, mineral grades, and particle size. This study investigates the development of a data-driven soft sensor to predict the silicate content in iron ore reverse flotation concentrate, a crucial indicator of plant performance. The proposed soft sensor model employs a dataset obtained from Kaggle, which includes measurements of iron and silicate content in the feed to the plant, reagent dosages, weight and pH of pulp, as well as the amount of air and froth levels in the flotation units. To reduce the dimensionality of the dataset, Principal Component Analysis, an unsupervised machine learning method, was applied. The soft sensor model was developed using three machine learning algorithms, namely, Ridge Regression, Multi-Layer Perceptron, and Random Forest. The Random Forest model, created with non-reduced data, demonstrated superior performance, with an R-squared value of 96.5% and a mean absolute error of 0.089. The results suggest that the proposed soft sensor model can accurately predict the silicate content in the iron ore flotation concentrate using machine learning algorithms. Moreover, the study highlights the importance of selecting appropriate algorithms for soft sensor developments in mineral processing plants.

Carbon Black Sensor and Neural Network Model for Sensing Angle in Soft Pneumatic Actuators

To solve the problem of low accuracy of soft sensor of monitoring variables due to strong nonlinear, multivariable coupling, parameters time-varying and large time delays in complex chemical process, a soft sensor modeling method based on self-organizing interval type-2 fuzzy neural network (SOIT2FNN) is proposed. Firstly, to solve the problem that the structure of interval type 2 neural network (IT2FNN) is difficult to determine, an algorithm for self-organizing generation rules that uses firing strength and rule similarity to define growth and deletion indicators is proposed. The algorithm uses the firing strength to determine whether to generate rules, and deletes the rules according to the similarity, thereby determining the structure of the interval type-2 fuzzy neural network. Secondly, the relevant parameters of the SOIT2FNN model are corrected by the gradient descent algorithm. Finally, SOIT2FNN is used as a soft sensor model to detect the tail oxygen concentration for uncatalysed oxidation of cyclohexane process. The experimental results show that the soft sensor method based on SOIT2FNN model has the advantages of timely detection and high detection accuracy.

High-precision prediction of material properties is an advanced direction of hot rolled product technology in manufacturing processes. However, complex disturbance usually produces wrong or missing data in the acquisition and entry stages. The long process and the diverse operating conditions bring great challenges to constructing soft sensors for the hot rolling process. To address this problem, a new time-series soft sensor model framework is proposed for mechanical properties prediction. Firstly, in order to process the raw dataset, the isolation forest algorithm is used to remove the outliers, and the random forest algorithm is used to fill in missing values. Secondly, the auxiliary variables are extracted by the combination of the XGBoost algorithm and prior mechanistic knowledge. Then, a DA-CBGRU-Seq2Seq time-series model based on a two-stage attention mechanism is designed for soft sensor modeling. In the encoder stage, external factors are introduced by an entity embedding layer. A combination structure of bidirectional gated recurrent units and convolutional layers is designed for extracting and learning the input features adaptively with the input attention mechanism. In the decoder stage, the long-term time dependence of the time series is learned by the temporal attention mechanism. Finally, the reliability of the proposed sensor model is compared and verified by the hot rolling process. The results indicate that the proposed method has an accuracy of over 95% in predicting the mechanical properties of a real hot-rolling process dataset, and has better performance compared to other comparative soft sensor prediction methods.

In industrial automation and intelligence, fault tolerance mechanisms have always been an attractive topic. To develop soft sensors with fault tolerance for different types of faults and unforeseen new faults, this article proposes a two-dimensional group distributionally robust optimization (2D-GDRO) framework for fault-tolerant soft sensor modeling. We propose to describe the potential distributions of new fault conditions with an uncertainty set and optimize the soft sensor model by minimizing the worst-case risk over the uncertainty set. Considering the restricted representation range of the uncertainty set constructed directly from a mixture distribution of a limited number of existing fault conditions in the training set, a two-dimensional uncertainty set is designed at the group dimension and the sample dimension. To efficiently train a fault-tolerant soft sensor within the 2D-GDRO framework, we introduce a triple-interleaved optimization algorithm. This algorithm integrates mini-batch stochastic gradient descent, exponentiated gradient ascent, and group-wise SoftMax techniques. Finally, the fault tolerance of the 2D-GDRO framework based soft sensor is verified using the Tennessee-Eastman process and the real three-phase flow facility. The experimental results show that 2D-GDRO outperforms other training frameworks in average soft sensing accuracy under new fault conditions.

Online quality prediction for cobalt oxalate synthesis process using least squares support vector regression approach with dual updating

Soft Sensor for Ammonia Concentration at the Ammonia Converter Outlet Based on an Improved Group Search Optimization and BP Neural Network