This article introduces a technique for monitoring chemical processes that are driven by a set of serially correlated nonstationary and stationary factors. The approach relies on (i) identifying and separating the common stationary and nonstationary factors, (ii) modeling these factors using multivariate time-series models, and (iii) incorporating a compensation scheme to directly monitor these factors without being compromised by the effect of forecast recovery. Based on the residuals of the time-series models, the technique yields two distinct test statistics to monitor both types of factors individually. In contrast to existing works, this article highlights that the technique is sensitive to any fault condition and can extract and describe both stationary and nonstationary trends. These benefits are illustrated by a simulation example and application of the approach to an industrial semibatch process describing nonstationary emptying and filling cycles.
This article introduces a framework to monitor complex dynamic and mildly nonstationary processes that are driven by a set of latent factors that can have different integration orders. The framework (i) relies on a novel deflation-based stationary subspace analysis that extracts latent source variables from recorded data sets in an iterative manner and (ii) utilizes the exact local Whittle estimator to calculate the fractional integration orders of the extracted source variables. The framework is embedded within a multivariate time-series structure to model the dynamic characteristics of the latent factors and to remove serial correlation in order to construct univariate monitoring statistics. A numerical and an industrial case study show that this framework is capable of modeling dynamic and mildly nonstationary variable inter-relationships that can have different integration orders.
This article introduces a revised common trend framework to monitor nonstationary and dynamic trends in industrial processes and shows needs for each improvement on the basis of three application studies. These improvements relate to (i) the extension of the common trend framework to include sets that contain stationary and nonstationary variables, (ii) handling cases where residuals are not drawn from multivariate normal distributions and (iii) the application of the framework to larger variable sets. Existing work does not adequately address these practically important issues. Industrial application studies highlight the needs for (i) the extended framework to model data sets containing stationary and nonstationary variables, (ii) handling statistics that are not based on normally distributed residuals and (iii) the use of Chigira procedure to robustly extract common trends. The extended framework is compared to traditional approaches. Keywords common trends models; Kasa decomposition; cointegration; latent stationary and nonstationary factors; generalized data structure; forecast recovery; multivariate normal distribution processes has been presented through the application to a glass melter process (Lin, Kruger & Chen, 2017), the following practically relevant issues have not been considered: the application studies presented herein contain recorded variable sets that are both, nonstationary and stationary, whereas Lin, Kruger & Chen (2017) addressed the problem of variable sets that are nonstationary only; the model residuals may not be drawn from multivariate normal distributions, in contrast to the work in Lin, Kruger & Chen (2017) where this assumption is made; and the conventional cointegration testing procedure by Johansen (1995) may run into difficulties if the number of variables is large, which is typically the case for complex industrial processes.This article is divided into the following sections. Section 2 gives a detailed description of the processes, including the FCCU simulator, the polymerization and the distillation process, used in this article. Section 3 then summarizes the monitoring framework and introduces an improved common trends framework. Sections 4 to 6 summarize the applications to the three processes. A concluding summary is given in Section 7. Process DescriptionsThis section provides a detailed description of the three processes that are used to demonstrate the working of the improved cointegration framework. Subsection 2.1 gives a description of the simulated fluid catalytic cracking unit. Subsections 2.2 and 2.3 then provide details of the polymerization and distillation processes, respectively. Fluid Catalytic Cracking UnitA fluid catalytic cracking unit (FCCU) is an important part of a refinery. An FCCU receives several different heavy feed stocks from other refinery units and cracks these into more valuable components that are usually blended into gasoline and other products. The main feed stream to an FCCU is gas oil, but heavier diesel and wash oil streams also cont...
The paper explains a concept of a vehicle molecular spring suspension whose stiffness in middle stage can be as low as 13 N/mm. The design of this suspension spring on the basis of a hydrophobic nanoporous material is introduced. The test methods of determining the static and dynamic mechanical properties of the novel suspension spring are described. The rationality of experimental design and the accuracy of theoretical analysis is proved by the negligible error between experimental results and theoretical analysis. The vibration isolation test results show that the natural frequency of the suspension can be as low as 1.06 Hz.
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