Jingyun Xu

Multi‐rate data are common in industrial processes and pose significant challenges for robust soft sensing. Although the multi‐rate pyramid variational autoencoder regression model has been developed to handle such data, it still suffers from latent variable feature entanglement and noise‐sensitive information propagation. To address these issues, this paper proposes a bidirectional gated feature pyramid network‐decoupled variational autoencoder for robust soft sensing in multi‐rate industrial processes. The proposed model decouples process data into quality‐relevant and quality‐irrelevant latent variables across multiple time scales. A mutual information maximization term is introduced to preserve key quality‐related information, thereby mitigating feature entanglement. In addition, a bidirectional gated fusion pyramid network is designed, which integrates top‐down semantic and bottom‐up detail streams and employs learnable gates to enable adaptive cross‐resolution fusion and effective noise suppression. Experimental results on numerical and industrial benchmark datasets demonstrate that the proposed method achieves superior prediction accuracy and robustness over mainstream approaches, offering an effective solution for multi‐rate soft sensing applications.

Existing quality-relevant stationary subspace analysis methods suffer from significant performance degradation in the presence of outliers in industrial processes, primarily due to the failure of Gaussian distribution assumptions. Additionally, these methods do not account for the dynamic correlations between adjacent time-series samples, leading to suboptimal model performance. To address these issues, this paper proposes a Dynamic Robust Projection to Stationary Subspace Regression for Quality Prediction (DRPSSR).First, process variables are decoupled into quality-relevant stationary, quality-relevant non-stationary, quality-irrelevant stationary, and quality-irrelevant non-stationary latent variables, thereby reducing interference from quality-irrelevant information in the dynamic transmission and prediction of quality-related information. Leveraging the heavy-tailed property of the t-distribution, the Gaussian distribution assumption for latent space parameters is replaced with a t-distribution to enhance the model’s robustness to outliers. Furthermore, considering that Long Short-Term Memory (LSTM) networks balance long-term memory and short-term inputs through gating mechanisms and cell states, an LSTM is introduced to model historical quality-relevant stationary and non-stationary latent variables as state variables, enabling the propagation of dynamic information.Numerical simulations and an industrial case study on a debutanizer column demonstrate that the proposed model significantly improves prediction accuracy on industrial datasets containing outliers, validating its effectiveness and engineering applicability for soft sensor modeling in complex industrial processes.

State of Charge (SOC) estimation for lithium-ion batteries is a critical component of battery health management systems. Accurate SOC estimation is essential for ensuring the safe operation of batteries. However, SOC estimation is a multimodal, nonlinear, and non-Gaussian problem. Given that particle filters are highly effective in modeling nonlinear and non-Gaussian systems, and that the t-distribution exhibits heavy-tailed characteristics, this paper proposes an iterative SOC estimation method based on a developed multivariate joint t-distribution particle filter(DMT-PF). First, a dual-polarization equivalent circuit model is used to construct the state and observation equations for SOC estimation. A novel observation is made that the state variables involved in SOC estimation are correlated. To address this, a multivariate t-distribution is used to model the state probability density function, enabling accurate state estimation and effective resampling, thereby mitigating particle degeneracy while keeping computational cost manageable. Furthermore, when large fluctuations occur between adjacent SOC estimates, an adaptive iterative strategy is introduced to adjust the scale matrix of the t-distribution, effectively reducing estimation errors caused by frequent disturbances. Experimental results demonstrate that the proposed method outperforms conventional approaches in terms of both estimation accuracy and robustness, particularly under frequent mode-switching scenarios.

Soft sensor technology is increasingly crucial for quality control in modern industrial processes. However, as industrial systems grow more complex, they begin to exhibit intricate characteristics such as nonstationary, uncertainty, and dynamic. These complexities pose significant challenges to conventional data‐driven soft sensor modelling approaches. In response, researchers have explored methods like stationary subspace analysis (SSA), probabilistic stationary subspace analysis (PSSA), and hidden Markov model (HMM) to handle nonstationary, uncertain, and dynamic process data. Nonetheless, each of these methods fails to fully capture these characteristics of complex industrial processes, which in turn limits their predictive performance. To overcome these limitations, this chapter introduces a probabilistic dynamic stationary subspace regression (PDSSR) soft sensor model tailored to nonstationary industrial processes. Specifically, the proposed model first decomposes the latent variables into quality‐related and quality‐unrelated components according to their relevance to the product quality variables. Next, within a stationary subspace analysis framework, the quality‐related information is further partitioned into stationary and nonstationary components, thereby accurately capturing nonstationary characteristics. Moreover, during the online estimation process, a hidden Markov chain inference mechanism is incorporated to enhance the accuracy of parameter estimation by accounting for regime changes over time. Finally, Numerical example and a case study on a debutanizer distillation column demonstrate that the proposed method achieves high predictive accuracy in soft sensing for complex, nonstationary industrial processes.

In recent years, the Mixture Variational Autoencoder (MVAE) model has been widely applied in industrial process monitoring and soft sensor modeling due to its strong feature extraction capabilities for multimodal data. However, the traditional MVAE, as an unsupervised generative model, often contains a large amount of irrelevant information during feature extraction, which is not conducive to predicting quality variables. To address this issue, a soft sensor modeling method based on quality-related Mixture Variational Autoencoder Regression (MVAE-R) is proposed and applied to complex multimodal industrial processes. This method first maps the process variables into two subspaces through nonlinear mapping: a quality-independent subspace and a quality-related subspace. It then extracts the prior information on these two subspaces from both process and quality variables, which better separates the latent variables related and unrelated to quality, effectively capturing the nonlinear features that are highly correlated with the target quality variable. Subsequently, the latent variables under each modality are learned to obtain an effective feature representation of the process variables while predicting the quality variables. Finally, the performance of the proposed model is evaluated through a numerical example and a real industrial case, demonstrating the model's effectiveness and superiority.

Lithium-ion batteries, being the main energy source for electric vehicles, need precise State of Charge (SOC) estimation to maintain system reliability. Traditional methods for SOC estimation do not meet the desired accuracy for engineering applications. This study introduces an advanced approach for SOC estimation in lithium-ion batteries by utilizing Particle Swarm Optimization (PSO) enhanced Particle Filtering. At the outset, a second-order RC equivalent circuit model is developed, and its parameters are determined. Considering significant differences in the open-circuit voltage (OCV) and SOC curves during charging and discharging, three types of OCV-SOC fitting curves are designed to define the state and observation equations. In conclusion, a particle filter-based SOC estimation model is built, and an improved PSO method is introduced to optimize state value determination. The experimental outcomes indicate that the proposed method surpasses conventional SOC estimation techniques in performance.

To be prepared for the capacity diving phenomena in future capacity deterioration, a hybrid method for predicting the remaining useful life (RUL) of lithium-ion batteries (LIBs) is proposed. First, a novel empirical degradation model is proposed in this paper to improve the generalization applicability and accuracy of the algorithm. A particle filter (PF) algorithm is then implemented to generate the original error series using prognostic results. Next, a discrete wavelet transform (DWT) algorithm is designed to decompose and reconstruct the original error series to improve the data validity by reducing the local noise distribution information. A relatively less approximate component is selected as the reconstructed error series, which preserves the primary evolutionary information. Finally, to make full use of the information contained in the PF algorithm's prognosis results, the support vector regression (SVR) algorithm is utilized to correct the PF prognosis results. The results indicate that long-short-term deterioration progress and RUL prediction tasks can both benefit from significant performance improvements.