The dynamic characteristics of multiphase industrial processes present significant challenges in the field of industrial big data modeling. Traditional soft sensing models frequently neglect the process dynamics and have difficulty in capturing transient phenomena like phase transitions. To address this issue, this article introduces a causality-driven sequence segmentation (CDSS) model. This model first identifies the local dynamic properties of the causal relationships between variables, which are also referred to as causal mechanisms. It then segments the sequence into different phases based on the sudden shifts in causal mechanisms that occur during phase transitions. Additionally, a novel metric, similarity distance, is designed to evaluate the temporal consistency of causal mechanisms, which includes both causal similarity distance and stable similarity distance. The discovered causal relationships in each phase are represented as a temporal causal graph (TCG). Furthermore, a soft sensing model called temporal-causal graph convolutional network (TC-GCN) is trained for each phase, by using the time-extended data and the adjacency matrix of TCG. The numerical examples are utilized to validate the proposed CDSS model, and the segmentation results demonstrate that CDSS has excellent performance on segmenting both stable and unstable multiphase series. Especially, it has higher accuracy in separating non-stationary time series compared to other methods. The effectiveness of the proposed CDSS model and the TC-GCN model is also verified through a penicillin fermentation process. Experimental results indicate that the breakpoints discovered by CDSS align well with the reaction mechanisms and TC-GCN significantly has excellent predictive accuracy.

The task of uncovering causal relationships among multivariate time series data stands as an essential and challenging objective that cuts across a broad array of disciplines ranging from climate science to healthcare. Such data entails linear or non-linear relationships, and usually follow multiple a priori unknown regimes. Existing causal discovery methods can infer summary causal graphs from heterogeneous data with known regimes, but they fall short in comprehensively learning both regimes and the corresponding causal graph. In this paper, we introduce CASTOR, a novel framework designed to learn causal relationships in heterogeneous time series data composed of various regimes, each governed by a distinct causal graph. Through the maximization of a score function via the EM algorithm, CASTOR infers the number of regimes and learns linear or non-linear causal relationships in each regime. We demonstrate the robust convergence properties of CASTOR, specifically highlighting its proficiency in accurately identifying unique regimes. Empirical evidence, garnered from exhaustive synthetic experiments and two real-world benchmarks, confirm CASTOR's superior performance in causal discovery compared to baseline methods. By learning a full temporal causal graph for each regime, CASTOR establishes itself as a distinctly interpretable method for causal discovery in heterogeneous time series. Multivariate Time Series (MTS) is a very common type of data in a wide variety of fields. Uncovering the causal relationships among MTS variables and understanding how they evolve over time is crucial in numerous fields, such as climate science and health care. Although randomized controlled trials are widely recognized as the definitive method for determining causal relationships (Hariton & Locascio, 2018; McCoy, 2017), they often present challenges in terms of cost, ethics, or feasibility. For example: learning gene regulatory networks via gene knockout experiments would be prohibitively expensive on a large scale. Consequently, a multitude of causal discovery approaches now focus on extracting causality from observational data sources (L owe et al., 2022; Bussmann et al., 2021; Pamfil et al., 2020; Moraffah et al., 2021; Runge, 2018; Wu et al., 2020).

We propose a new approach for Temporal Diagnosis Problems. This approach is an extension of  Bouzid and Ligeza's  method for temporal diagnosis problems. In this latter work, the authors define a Temporal Causal Graph (TCG) where time delays are expressed as temporal instants. We extend the TCG by including two quantitative relations in order to handle temporal intervals. We call ExTCG this new model. Solving a temporal diagnosis problem represented by the ExTCG consists of finding all possible explanations. It is performed using a backtrack search algorithm. In many diagnosis applications, the generation of all possible explanations is not necessary. For this reason, we augment the ExTCG in order to consider the degree of causality between symptoms. We call weighted ExTCG this extended model. Solving it consists of finding the explanation  having the highest probability to occur. Through a real world diagnosis application in medicine, we illustrate the weighted ExTCG and its corresponding solving algorithm.

We propose a new approach for Temporal Diagnosis Problems. This approach is an extension of  Bouzid and Ligeza's  method for temporal diagnosis problems. In this latter work, the authors define a Temporal Causal Graph (TCG) where time delays are expressed as temporal instants. We extend the TCG by including two quantitative relations in order to handle temporal intervals. We call ExTCG this new model. Solving a temporal diagnosis problem represented by the ExTCG consists of finding all possible explanations. It is performed using a backtrack search algorithm. In many diagnosis applications, the generation of all possible explanations is not necessary. For this reason, we augment the ExTCG in order to consider the degree of causality between symptoms. We call weighted ExTCG this extended model. Solving it consists of finding the explanation  having the highest probability to occur. Through a real world diagnosis application in medicine, we illustrate the weighted ExTCG and its corresponding solving algorithm.