Missing data is a common phenomenon in the industrial field. The recovery of missing data is crucial to enhance the reliability of subsequent data-driven monitoring and control of industrial processes. Most existing methods are limited by the confined scope of feature extraction, which makes it impossible to rely on global information to impute missing data. In addition, they usually assume that industrial data is a uniform distribution across all working conditions, ignoring the differences in data evolution patterns across different conditions. To address these issues, this paper proposes an innovative scope-free global multi-condition-aware imputation framework based on diffusion transformer (SGMCAI-DiT). First, it extends the diffusion model by introducing conditional probability to capture the condition distribution of the entire data. Then, a noise prediction model is designed based on a novel double-weighted attention mechanism (DW-SA) to broaden the horizons of feature extraction. By discerning the inter-conditional interactions and the intra-conditional local information, the missing data imputation performance can be improved. Finally, the effectiveness and suitability of the proposed SGMCAI-DiT are verified on four real datasets sourced from industrial processes and two public non-industrial datasets. Extensive experimental results demonstrate that the proposed method outperforms several state-of-the-art methods in different missing data scenarios.

Multiple modes are ubiquitous in current industrial processes, and the amount of historical data contained in different modes may vary considerably. Insufficient data can easily lead to cold start problems when building a fault detection model for a particular mode. To solve this problem, while considering the similarity and differences between multiple modes, a deep model using domain adaptation based on feature separation is proposed for nonlinear process monitoring with few samples. The model extracts common features from modes and the data deficiency is compensated by transferring the domain knowledge from the source to the common features. On the other hand, to avoid missing useful information by focusing only on common features, the model also extracts the specific features of the target domain. Thus, monitoring performance is improved with the help of domain adaptation while taking into account the specific characteristics of the target domain. Furthermore, three detection indices are designed to monitor the common feature subspace, the specific feature subspace, and the residual subspace, respectively. The benefit of this is allowing more diagnostic information to be obtained when a fault occurs. The proposed method was tested with a numerical example and a real industrial hydrocracking process to verify the detection effectiveness.

Recommender systems are effective in predicting the most suitable products for users, such as movies and books. To facilitate personalized recommendations, the quality of item ratings should be guaranteed. However, a few ratings might not be accurate enough due to the uncertainty of user behavior and are referred to as natural noise. In this article, we present a novel fuzzy clustering‐based method for detecting noisy ratings. The entropy of a subset of the original ratings dataset is used to indicate the data‐driven uncertainty, and evaluation metrics are adopted to represent the prediction‐driven uncertainty. After the repetition of resampling and the execution of a recommendation algorithm, the entropy and evaluation metrics vectors are obtained and are empirically categorized to identify the proportion of the potential noise. Then, the fuzzy C‐means‐based denoising (FCMD) algorithm is performed to verify the natural noise under the assumption that natural noise is primarily the result of the exceptional behavior of users. Finally, a case study is performed using two real‐world datasets. The experimental results show that our proposal outperforms previous proposals and has an advantage in dealing with natural noise.