Soft Sensor Model Research Articles

Soft sensor model for endpoint carbon content and temperature in BOF steelmaking based on just-in-time learning with multilayer structure preservation and sparse information enhancement

Ensuring precise prediction of the endpoint carbon content and temperature is paramount in controlling the endpoint of the basic oxygen furnace (BOF) steelmaking process. However, due to the frequent fluctuations in real-time blowing conditions, the conventional just-in-time learning soft sensor approach encounters challenges in effectively anticipating the blowing endpoint. To address these aforementioned issues, this research introduces a novel approach known as the pattern-oriented multilayer structure preservation and sparse information enhancement model (POMLSP-SIE). This approach involves dynamically generating a dataset with the same distribution based on the characteristics of the query sample pattern. It is combined with a multi-pathway dimension reduction model to preserve multi-view spatial geometry information while reducing data dimension. The low-dimensional embedding serves as dictionaries containing various hierarchical structural characteristics. Significant information within these dictionaries is sparsely represented to amplify its influence during the regression prediction process while diminishing the impact of less relevant information. This refinement aims to rectify the problem of static regression models being weak to adapt to changing working conditions, ultimately enhancing prediction performance. The effectiveness of the proposed method is substantiated through an experimental study utilising real converter steelmaking process data, thereby confirming its practical applicability.

A Hybrid Soft Sensor Framework for Real-Time Biodiesel Yield Prediction: Integrating Mechanistic Models and Machine Learning Algorithms

Biodiesel yield prediction is vital for optimizing process efficiency, minimizing costs, and maintaining product quality. Traditional methods are labor-intensive, costly, and lack real-time capabilities, leading to inefficiencies in operations. Data-driven soft sensors offer real-time prediction but require extensive, high-quality datasets, posing practical challenges. To address these limitations, this study proposes a hybrid soft sensor model that integrates mechanistic and data-driven approaches. Mechanistic models were utilized to generate computational data via MATLAB®, reducing the reliance on costly laboratory experiments. A comprehensive dataset (n=1500) comprising seven input variables—catalyst type, feedstock type, temperature, reaction time, free fatty acid (FFA) content, water content, and methanol-to-oil ratio—along with one output variable (biodiesel yield) was developed. This dataset was used to train various machine learning algorithms, with the artificial neural network (ANN) model demonstrating the highest predictive accuracy, achieving an R2 (goodness of fit) of 0.998 and root mean square error (RMSE) of 0.303. Hyperparameter tuning further enhanced the model’s performance, reducing RMSE and the mean absolute error (MAE) by 63% and 61.7%, respectively. By combining mechanistic and data-driven techniques, this hybrid model effectively overcomes the limitations of traditional and purely data-driven methods, providing a cost-effective and efficient solution for biodiesel yield prediction and data generation.

Just-in-time framework for robust soft sensing based on robust variational autoencoder

Modeling with high-dimensional data subject to abnormal observations have always been a practical interest. In this paper, under the just-in-time learning (JITL) framework, a robust soft sensor modeling approach is developed based on robust Variational Autoencoder (VAE). Unlike the vanilla VAE that extracts features from the given dataset under the Gaussian prior assumption, robust VAE employs Student’s t-distribution as prior distribution to handle abnormal data. Under assumption of the Student’s t-prior, the proposed robust VAE model is capable of describing collected data contaminated with outliers. Once the robust VAE model is trained, each robust feature variable in the latent space can be determined. Subsequently, similarity measure is calculated using robust Kullback-Leibler divergence between two Student’s t-distributions, that is, the distribution of a new data sample and that of each historical data sample. After completing similarity measurement for a query sample, the weights for input-output historical data can be determined. Based on these weighted historical data samples, a robust probabilistic principal component regression (PPCR) is utilized to perform local modeling for prediction. Numerical simulations, including the Tennessee Eastman and Penicillin fermentation benchmark processes, are utilized to validate the proposed JITL-based robust soft sensor modeling method.

A Flame Image Soft Sensor for Oxygen Content Prediction Based on Denoising Diffusion Probabilistic Model

High-precision oxygen content measurement is crucial for statistical analysis of combustion chemical reaction. Deep learning based soft sensor is a new class of intelligent tools for monitoring combustion oxygen content. But in the actual production, data for sensors are often insufficient. A new soft sensing model is proposed to display the excellent performance of denoising diffusion probabilistic model (DDPM) in data generation. Firstly, a UNet based soft sensor is designed by integrating self-attention mechanism into the convolution layers. Then, a denoising loss function is designed to link the feature extraction process of soft sensor model with the reverse denoising process of DDPM, and the noise prediction neural network of DDPM is used to improve the feature extractability of the soft sensor model. Finally, the proposed model is compared with common models. The effectiveness and superiority of the proposed soft sensing model for oxygen content prediction, especially in the case with a small sample size, are both confirmed by the results.

Batch process soft sensing based on data-stacking multiscale adaptive graph neural network

Abstract Soft sensing technology has found extensive application in predicting key quality variables in batch processes. However, its application in batch process is limited by the uneven batch length, the correlation of data and the difficulty in extracting the dependencies between variables and within variables. To address these issues, we propose a data-stacking multiscale adaptive graph neural network (DSMAGNN) soft sensor model. Firstly, Mutual information (MI) is used to selected quality-related variables, the 3D batch data is converted into a time-delay sequence suitable for input to the soft sensor model through the data stacking strategy, and the underlying time correlation at different time scales is preserved by incorporating the multi-scale pyramid network. Secondly, the dependencies between variables are inferred by the adaptive graph learning module, while the dependencies both within and between variables are modeled by the multi-scale temporal graph neural network. Thirdly, collaborative work across different time scales is further facilitated by the scale fusion module. Finally, the feasibility and effectiveness of the model are verified through experiments in the industrial-scale penicillin fermentation process and hot rolling process. (DSMAGNN) soft sensor model. Firstly, MI is used to selected quality-related variables, and the data stacking strategy is employed to convert 3D batch data into a time-delay sequence suitable for input to the soft sensor model. A multiscale pyramid network is utilized to preserve the underlying time dependence across different time scales. Secondly, since the dependence relationship between variables may vary across different time scales, the adaptive graph learning modules deduce scale-specific variable dependencies without relying on predefined priors. Thirdly, given the multiscale feature representation and the inferred dependency relationships between scale-specific variables, we introduce a multiscale temporal graph neural network to jointly model dependencies within and between variables. Building upon this foundation, the scale fusion module is deployed to facilitate collaboration across different temporal scales and automatically capture the significance of contributing temporal patterns. We validate the feasibility and effectiveness of the proposed model through experiments conducted in industrial-scale penicillin fermentation and hot continuous rolling processes, the results show that the proposed model is superior to several compared models, thus confirming its validity.

Soft-sensor model development for CHO growth/production, intracellular metabolite, and glycan predictions.

Efficaciously assessing product quality remains time- and resource-intensive. Online Process Analytical Technologies (PATs), encompassing real-time monitoring tools and soft-sensor models, are indispensable for understanding process effects and real-time product quality. This research study evaluated three modeling approaches for predicting CHO cell growth and production, metabolites (extracellular, nucleotide sugar donors (NSD) and glycan profiles): Mechanistic based on first principle Michaelis-Menten kinetics (MMK), data-driven orthogonal partial least square (OPLS) and neural network machine learning (NN). Our experimental design involved galactose-fed batch cultures. MMK excelled in predicting growth and production, demonstrating its reliability in these aspects and reducing the data burden by requiring fewer inputs. However, it was less precise in simulating glycan profiles and intracellular metabolite trends. In contrast, NN and OPLS performed better for predicting precise glycan compositions but displayed shortcomings in accurately predicting growth and production. We utilized time in the training set to address NN and OPLS extrapolation challenges. OPLS and NN models demanded more extensive inputs with similar intracellular metabolite trend prediction. However, there was a significant reduction in time required to develop these two models. The guidance presented here can provide valuable insight into rapid development and application of soft-sensor models with PATs for ipurposes. Therefore, we examined three model typesmproving real-time product CHO therapeutic product quality. Coupled with emerging -omics technologies, NN and OPLS will benefit from massive data availability, and we foresee more robust prediction models that can be advantageous to kinetic or partial-kinetic (hybrid) models.

Comparative analysis and application of soft sensor models in domestic wastewater treatment for advancing sustainability

ABSTRACT This study focuses on the development and evaluation of soft sensor models for predicting NH3-N values in a wastewater treatment process. The study compares the performance of linear regression (LR), neural networks (NN) and random forest regression (RFR) models. The proposed methodology involves optimizing the sequencing batch reactor process using artificial intelligence and an automatic control system. Real-time NH3-N values are obtained by inputting data from electronic conductivity and temperature sensors into the prediction models. Once the predicted NH3-N value falls below the effluent standard, the cycle ends, improving energy efficiency and sustainability by cutting down the agitator and aerator. The research results demonstrate that the RNN-based NH3-N soft sensor built in this study exhibits the best performance, which is promising for wastewater treatment process optimization and evaluation. The results show that sensor model NNR[0.5Y]H exhibits exceptional performance, utilizing recurrent neural network with 5-step input delays. Sensor NNR[0.5Y]H exhibits an R2 of 0.921, an RMSE of 6.110, and an MAE of 4.558. Based on the findings, recurrent neural network (RNN) variants emerge as the most effective modeling technique due to their ability to capture temporal dependencies and handle variable-length sequences. This study provides satisfied performance results for the NNR[0.5Y]H soft sensor model in NH3-N monitoring and process optimization in wastewater treatment, highlighting the effectiveness of recurrent neural networks and their contribution to improving interpretability, accuracy, and adaptability of soft sensor models.

Soft sensor modeling method and application based on TSECIT2FNN-LSTM

To address the issue of low accuracy in soft sensor modeling of key variables caused by multi-variable coupling and parameter sensitivity in complex processes, this paper introduces a TSK-type-based self-evolving compensatory interval type-2 fuzzy Long short-term memory (LSTM) neural network (TSECIT2FNN-LSTM) soft sensor model. The proposed TSECIT2FNN-LSTM integrates the LSTM neural network with the interval type-2 fuzzy inference system to address long-term dependencies in sequence data by utilizing the gate mechanism of the LSTM neural network. The TSECIT2FNN-LSTM structure learning algorithm uses the firing strength of the network rule antecedent to decide whether to generate new rules to improve the rationality of the network structure. TSECIT2FNN-LSTM parameter learning utilizes the gradient descent method to optimize network parameters. However, unlike other interval type-2 fuzzy neural network gradient calculation processes, the error term in the LSTM node parameter gradient of TSECIT2FNN-LSTM is propagated backwards in the time dimension. Additionally, the error term is simultaneously transferred to the upper layer network to enhance network prediction accuracy and memory capabilities. The TSECIT2FNN-LSTM soft sensor model is utilized to predict the alcohol concentration in wine and the nitrogen oxide emission in gas turbines. Experimental results demonstrate that the proposed TSECIT2FNN-LSTM soft sensing model achieves higher prediction accuracy compared to other models.

Adaptive fuzzy coordinated control design for wind turbine using gray wolf optimization algorithm

Due to the randomness and intermittency of wind speed, the actual output power curve of a wind turbine (WT) deviates greatly from the theoretical power curve, thereby reducing the power generation capacity of the WT. An adaptive fuzzy coordinated control (AFCC) of WT is presented in this study to improve the power generation of WT. Firstly, a multi-objective optimization model (MOOM) for WT output power, generator speed and pitch angle is established, and its optimal solution set is used as the input eigenvector of a novel effective wind speed soft sensor (NEWSSS) model, which is modeled with kernel extreme learning machine (KELM). Secondly, a novel improved gray wolf optimization (NIGWO) algorithm is presented by improving the convergence factor and adaptive weights, which is used to solve MOOM and optimize the parameters of KELM. A variable pitch control (VPC) is designed by estimating the effective wind speed. Finally, an adaptive fuzzy control (AFC) is presented for WT. Based on the AFC and VPC, an AFCC for pitch angle and generator torque is designed for WT. The high measuring precision of NEWSSS and the good robustness and dynamic performance of AFCC are demonstrated by the simulation results.

A physics‐constrained hybrid residual neural network for the prediction of moisture content in a closed‐cycle drying system

AbstractClosed‐cycle drying technology has the advantages of safety, energy saving, and environmental protection, and has a wide application prospect. Due to the multi‐physics and multi‐scale nature of heat/mass transfer in the closed‐cycle drying process, as well as the characteristics of drying medium circulation and energy integration, it is difficult to obtain the product moisture content prediction model in closed‐cycle process based on rigorous closed‐cycle drying process mechanism model. However, accurate monitoring of product moisture content in the closed‐cycle drying process is the key to improving drying quality and process optimization. Aiming at the challenges in predicting moisture content, this paper proposes a physics‐constrained hybrid residual neural network (PC‐HRNN) for soft sensor modelling within a designed closed‐cycle drying system. The characteristic of this proposed method lies in its effective fusion of physics, knowledge, and data. First, a hybrid residual neural network (HRNN) is constructed based on the integration of a physics model and a data‐driven model. The HRNN takes the knowledge from the physics model as its auxiliary features and learns the prediction residuals of the physics model through a neural network model. Then, a new loss function that takes into account physical laws is introduced into HPNN to standardize model training and improve the generalization performance of the model. The experimental results show that the PC‐HRNN model improves prediction accuracy and model robustness, reduces the demand for data, and demonstrates stronger extrapolation capabilities under limited data.

A novel self-training framework for semi-supervised soft sensor modeling based on indeterminate variational autoencoder

In modern industrial processes, the high acquisition cost of labeled data can lead to a large number of unlabeled samples, which greatly impacts the accuracy of traditional soft sensor models. To this end, this paper proposes a novel semi-supervised soft sensor framework that can fully utilize the unlabeled data to expand the original labeled data, and ultimately improve the prediction accuracy. Specifically, an indeterminate variational autoencoder (IVAE) is first proposed to obtain the pseudo-labels of unlabeled data as well as their uncertainty. On this basis, the IVAE-based self-training (ST-IVAE) framework is further naturally proposed to expand the original small labeled dataset through continuous circulation. Among them, a variance-based oversampling (VOS) strategy is introduced to better utilize the pseudo-label uncertainty. By determining similar sample sets through the comparison of Kullback-Leibler (KL) divergence obtained by the proposed IVAE model, each sample can be independently modeled for prediction. The effectiveness of the proposed semi-supervised framework is verified on two real industrial processes and the realization results illustrate that the ST-IVAE framework can still predict well even in the presence of missing input data compared to state-of-the-art methodologies in addressing semi-supervised soft sensing challenges.

Soft sensor modeling based on self-organizing fuzzy neural network with clustering, merging, and splitting scheme

Abstract As a pivotal role in the control, optimization, and monitoring of contemporary industrial processes, soft sensors are frequently employed in the prediction of key quality variables. To achieve accurate prediction of key quality variables in industrial processes, a soft sensor modeling method based on the self-organizing fuzzy neural network with the clustering, merging, and splitting scheme (SOFNN-CMS) is proposed. First, the supervised fuzzy C-means clustering algorithm is proposed to identify the appropriate initial center and width of the fuzzy neural network, obtaining appropriate initial fuzzy rules. Then, a neuron merging and splitting strategy is designed to adjust the structure of the fuzzy neural network, by merging and splitting the hidden neurons according to the distance of clusters, increasing the adaptability of the fuzzy neural network. Besides, to accelerate the convergence of estimation errors, an improved Levenberg Marquardt algorithm is utilized to update neural network parameters in the training phase, realizing the soft sensor modeling of key quality variables. The effectiveness of the proposed SOFNN-CMS neural network is demonstrated on two benchmark problems and an industrial debutanizer column. Finally, the experiments showcase that the proposed SOFNN-CMS neural network can obtain better soft sensor modeling performance with a compact structure.

Global dynamic features and information of adjacent hidden layer enhancement based on autoencoder for industrial process soft sensor application

AbstractThere is a lack of consideration of temporal and spatial correlation in the process variables and adjacent hidden layers correlation in the soft sensor model of stacked autoencoders. To address the issue, a novel global dynamic adjacent layer information enhancement auto encoder (GD‐ALIEAE) method is proposed to improve the poor prediction performance. The gated recurrent unit (GRU) and uniform manifold approximation and projection (UMAP) are applied to the GD‐ALIEAE model for obtaining global dynamic features of the temporal and spatial information of process variables by parallel computation. An adjacent layer information correlation algorithm is proposed to avoid the loss of hidden layers information during the stacking process. The algorithm enhances the features of the low layer through nonlinear mapping, combining the low layer and its adjacent layer as input. The input then is fed to the multi‐head attention mechanism to obtain features that contain adjacent layer correlation. Finally, a prediction model is established through a fully connected layer. Through simulation experiments on two industrial cases of sulphur recovery unit and thermal power plant, and compared with models of stacked autoencoder (SAE), stacked isomorphic autoencoder (SIAE), and target‐related stacked autoencoder (TSAE), the effectiveness of the proposed method was verified.

Prediction interval soft sensor for dissolved oxygen content estimation in an electric arc furnace

In this study, a novel soft sensor modeling approach using Takagi–Sugeno (TS) fuzzy models and Prediction Intervals (PIs) is presented to quantify uncertainties in Electric Arc Furnace (EAF) steel production processes, namely to estimate the dissolved oxygen content in the steel bath. In real EAF operation, dissolved oxygen content is measured only a few times in the refining stage; therefore, the approach addresses the challenge of predicting unobserved output under conditions of irregular and scarce output measurements, using two distinct methods: Instant TS (I-TS) and Input Integration TS (II-TS). In the I-TS method, the model is computed for each individual indirect measurement, while the II-TS approach integrates these indirect measurements. The inclusion of PIs in TS models allows the derivation of the narrowest band containing a prescribed percentage of data, despite the presence of heteroscedastic noise. These PIs provide valuable insight into potential variability and allow decision-makers to evaluate worst-case scenarios. When evaluated against real EAF data, these methods were shown to effectively overcome the obstacles posed by scarce output measurements. Despite its simplicity, the I-TS model performed better in terms of interpretability and robustness to the operational reality of the EAF process. The II-TS model, on the other hand, showed excellent performance on all metrics but exhibited theoretical inconsistencies when deviating from typical operations. In addition, the proposed method successfully estimates carbon content in the steel bath using the established dissolved oxygen/carbon equilibrium, eliminating the need for direct carbon measurements. This shows the potential of the proposed methods to increase productivity and efficiency in the EAF steel industry.

Graph semi-supervised soft sensor modeling based on label propagation algorithm

Abstract Data-driven soft sensor modeling methods have become prevalent in the industry. Nonetheless, the complexity of industrial processes often leads to the absence or difficulty in obtaining key labeled data, and existing methods frequently fail to fully utilize the inherent correlations between variables. This paper proposes a novel graph semi-supervised soft sensor modeling method using the label propagation algorithm to address these issues. This method utilizes correlations within the data to assign pseudo-labels to unlabeled data reasonably and employs Graph Convolutional Networks (GCN) to capture spatial relationships between nodes. Additionally, by embedding a Long Short-Term Memory (LSTM) structure, the model can capture temporal dependencies of the data while focusing on spatial structures. Furthermore, the introduction of a residual structure enables the model to directly learn the differences between inputs and outputs, facilitating information transmission, and improving the model's feature extraction ability. Experiments demonstrate the effectiveness of the method.

Research on a semi-supervised soft sensor modelling method for complex chemical processes based on INGO-VMD-ESN

Abstract The dynamic and non-linear nature of complex chemical processes often leads to low prediction accuracy of key quality variables by traditional soft sensors, thus affecting the overall system control accuracy and operational efficiency. Therefore, this paper proposes a semi-supervised soft sensor modelling method based on improved the northern goshawk optimization (INGO)-variable mode decomposition (VMD)-echo state network (ESN). Firstly, a new semi-supervised fusion method is proposed to address the problem of model training difficulty due to the scarcity of labelled samples and process dynamics, which reconstructs the sample dataset by fusing labelled and unlabelled samples into more representative new samples, improving the model’s generalization ability. Secondly, for the noise interference present in the reconstructed data, the input data is denoised using the VMD method to improve the quality of data. Then, a soft sensor model is built based on ESN. Additionally, the denoising and prediction performance of VMD and ESN is significantly affected by parameters, therefore the paper utilizes the INGO algorithm to achieve parameter rectification for VMD and ESN. Finally, the method is validated based on actual sulphur recovery data from a refinery. The results demonstrate that the method effectively mitigates the impact of dynamics and nonlinearity in the complex chemical process which enhances prediction accuracy.

Dynamic Soft Sensor Model for Endpoint Carbon Content and Temperature in BOF Steelmaking Based on Adaptive Feature Matching Variational Autoencoder

The key to endpoint control in basic oxygen furnace (BOF) steelmaking lies in accurately predicting the endpoint carbon content and temperature. However, BOF steelmaking data are complex and change distribution due to variations in raw material batches, process adjustments, and equipment conditions, leading to concept drift and affecting model performance. In order to resolve these problems, this paper proposes a dynamic soft sensor model based on an adaptive feature matching variational autoencoder (VAE-AFM). Firstly, this paper innovatively proposes an adaptive feature matching (AFM) method. This method utilizes the maximum mean discrepancy to calculate the values of the marginal and conditional distributions. Based on the discrepancy between these two values, a dynamic adjustment algorithm is designed to adaptively assign different weights to the two distributions. This approach dynamically and quantitatively evaluates and adjusts the relative importance of different distributions in the domain adaptation process, thereby enhancing the effectiveness of cross-domain data alignment. Secondly, a variational autoencoder (VAE) is employed to process the data, as the VAE model can capture the complex data structures and latent features in the steelmaking process. Finally, the features extracted by the VAE are processed with the adaptive feature matching method, thereby constructing the VAE-AFM dynamic soft sensor model. Experimental studies on actual BOF steelmaking data validate the efficacy of the offered approach, offering a reliable solution to the challenges of high complexity and concept drift in BOF steelmaking data.

Semi-supervised soft sensor method for fermentation processes based on physical monotonicity and variational autoencoders

Data-driven models have shown broad application prospects in soft sensor modeling. However, numerous challenges persist. On the one hand, data-driven soft sensor methods have high requirements on data quality. On the other hand, models relying on limited experimental data often lack physical interpretability. To tackle these challenges, a semi-supervised soft sensor method (PMVAER) for fermentation processes based on physical monotonicity and variational autoencoders (VAEs) is introduced. First, physical monotonicity constraint is incorporated into the loss function of VAEs for regression to ensure that the model's predictions adhere to physical feasibility. Next, considering the disparate sampling frequencies for process and quality variables, this approach is extended to learn from unlabeled data, creating a semi-supervised soft sensor model. The proposed model is validated on simulation and real cases of penicillin fermentation. Comparisons with five other methods verify that the proposed method exhibits exceptional predictive accuracy along with enhanced generalization ability.

Dual temporal attention mechanism-based convolutional LSTM model for industrial dynamic soft sensor

Abstract Deep learning is an appropriate methodology for modeling complex industrial data in the field of soft sensors, owing to its powerful feature representation capability. Given the nonlinear and dynamic nature of the process industry, the key challenge for soft sensor technology is to effectively mine dynamic information from long sequences and accurately extract features of relevance to quality. A dual temporal attention mechanism-based convolutional long short-term memory network (DTA-ConvLSTM) under an encoder-decoder framework is proposed as a soft sensor model to acquire quality-relevant dynamic features from serial data. Considering different influences of process variables for prediction at multiple time steps and various locations, ConvLSTM and temporal self-attention mechanism are utilized as the encoder to adaptively fuse spatiotemporal features and capture long-term dynamic properties of process in order to capture the trends of industrial variables. Furthermore, a quality-driven temporal attention mechanism is employed throughout the decoding process to dynamically select relevant features to more accurately track quality changes. The encoder-decoder model meticulously analyses the interactions between process and quality variables by incorporating dual-sequence dynamic information to improve the prediction performance. The validity and superiority of the DTA-ConvLSTM model was validated on two industrial case studies of the debutanizer column and sulfur recovery unit. Compared to the traditional LSTM model, the proposed model demonstrated a substantial improvement with the accuracy R2 up to 97.3% and 94.9% and the root mean square error reducing to 0.122 and 0.022.

Advanced soft-sensing techniques for predicting furnace temperature in industrial organic waste gasification

Accurately real-time monitoring furnace temperature in multi-component industrial organic waste gasification presents considerable challenges due to the process’s inherent complexity and variability. Herein, we have developed a sophisticated soft-sensing model that utilizes data-driven methods for precise temperature prediction, using input variables measured in industrial process. The data, primarily centered on cooling water, were derived from an in-depth analysis of heat transfer within the gasifier. Three distinct machine learning models were constructed and demonstrated enhanced performance compared to conventional heat transfer model. The Back Propagation Neural Network (BPNN) model, exhibiting a remarkable R2 value of 0.94, emerged as the most effective. Employing SHapley Additive exPlanations (SHAP) and Partial Dependence Plots (PDP), we further revealed the critical role of cooling water temperature in furnace temperature prediction. Overall, the application of data-driven models into the furnace temperature prediction offers a significant advancement in handling the complexities inherent in industrial processes.