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For nearly a decade, quality-related fault detection algorithms have been widely used in industrial systems. However, the majority of these detection strategies rely on static assumptions of the operating environment. In this paper, taking the time series of variables into consideration, a dynamic kernel entropy component regression (DKECR) framework is proposed to address the instability of quality-related fault detection due to the existing dynamic characteristics. Compared with the typical kernel entropy component analysis method, the proposed method constructs the relationship between process states and quality states to further interpret the direct effect on the product taken by the fault. In the proposed approach, process measurements are converted to a lower-dimensional subspace with a specific angular structure that is more comprehensive than traditional subspace approaches. In addition, the angular statistics and their relevant thresholds are exploited to enhance the quality-related fault detection performance. Finally, the proposed method will be compared with three methods by means of a numerical example and two industrial scenarios to demonstrate its practicality and effectiveness. Note to Practitioners—This paper studies a quality-related fault detection problem for the dynamic nonlinear industrial system. Controlling and measuring the quality state is challenging for the high-level monitoring system of the manufacturing process due to the nonlinear dynamic feature in states. This paper proposes a new data-driven method based on the kernel entropy component analysis method to assess the correlation between the quality and fault in the industrial system, reducing unnecessary overhaul and maintenance. Based on the autoregressive moving average exogenous algorithm, the proposed method captures the dynamic interaction between the process states to decrease false alarms. In the experimental section, the DKECR method outperforms the compared approaches, which can provide stable fault detection results. Additionally, the unique angle structure of the proposed method can supply more information for engineers’ monitoring needs. [ABSTRACT FROM AUTHOR]

We introduce an entropic segmentation algorithm and apply it to decompose the financial sequences into compositionally homogeneous domains. To probe more about the nature of the financial time series, we investigate the statistical properties of the segment from the view of segmentation position and segment length first. We reveal some important and interesting conclusions and information hidden in these time series of stock markets. Then, we focus on the study of the intrinsic properties for each segment in the time series from two aspects: time irreversibility and correlation. The fluctuations on the time irreversibility and the scaling exponent all support that the segments present compositional heterogeneity and verify the segmentation. Meanwhile, we conclude that time irreversibility is inherent in the stock time series and verifies that stock markets are nonequilibrium systems essentially even though segmentation. Moreover, the scaling exponents for each segment point out that the traditional detrended fluctuation analysis is not applicable to measure the correlation for the whole original time series of stock market. [ABSTRACT FROM AUTHOR]