This article investigates the state interval estimation problem for discrete-time linear time-varying descriptor systems subject to unknown but bounded system uncertainties. We propose a zonotope-based interval estimation method in an optimization framework. First, we present a novel zonotope-based interval estimator structure, in which the estimated interval bounds of each state component have design parameters independent of those of the other state components. Then, the widths of the jointly estimated intervals enclosing every state component are simultaneously minimized by solving parallel $L_{1}$ optimization problems via linear programming. Finally, a simulation study shows the effectiveness and higher accuracy of the proposed method compared with existing methods.

The whole process of the petrochemical industry involves flammable and explosive dangerous goods. The timely discovery of abnormalities or failures in the petrochemical process is crucial to ensure production safety. This paper sets up the approach to build the Digital Twin System (DTs) of a petrochemical process. Specifically, we decompose the petrochemical process into five levels one by one and build a digital twin plug-in for each component of the component layers, and then inversely decouple the process to assemble the DTs layer by layer. As a specific experimental example, the characteristic DTs is proposed to build modules of temperature field and pressure field and flow field, these DT modules are driven by practical industrial sampling data from cracking furnace, and three characteristic DTS modules stated above are integrated to form DTS. Based on the digital twin technology and DTs, we propose the logical structure of chemical process status monitoring and fault diagnosis in detail, which improves the safety and controllability of the petrochemical process.

Dynamic system fault diagnosis is often faced with a large number of possible faults. The purpose of this paper is to propose an efficient method for such situations. To avoid intractable combinatorial problems, sparse estimation techniques appear to be a powerful tool for isolating faults, under the assumption that only a small number of possible faults can be simultaneously active. However, sparse estimation is often studied in the framework of linear algebraic equations, whereas model-based fault diagnosis is usually investigated for dynamic systems modeled with state equations involving internal states. The main contribution of this paper is a link between these two formalisms through efficient and reliable algorithms, mainly relying on advanced analyses of residuals generated with the Kalman and Kitanidis filters. Based on these results, it becomes straightforward to solve fault diagnosis problems by applying well known sparse estimation techniques, in the framework of general time varying state-space systems involving unknown inputs.

Digital image correlation techniques are well known for motion extraction from video images. Following a two-stage approach, the pixel-level displacement is first estimated by maximizing the cross-correlation between two images, then the estimation is refined in the vicinity of the cross-correlation peak. Among existing subpixel refinement methods, quadratic surface fitting (QSF) provides good performances in terms of accuracy and computational burden. It estimates subpixel displacement by interpolating cross-correlation values with a quadratic surface. The purpose of this paper is to analytically investigate the QSF method. By means of counterexamples, it is first shown in this paper that, contrary to a widespread intuition, the quadratic surface fitted to the pixel-level cross-correlation values in the neighborhood of the cross-correlation peak does not always have a maximum. The main contribution of this paper then consists in establishing the mathematical conditions ensuring the existence of a maximum of this fitted quadratic surface, based on a rigorous analysis. Algorithm modifications for handling the failure cases of the QSF method are also proposed in this paper, in order to consolidate it for subpixel motion extraction. Experimental results based on two typical types of images are also reported.

The stability of the Kalman filter, though less often mentioned than the optimality in the recent literature, is a crucial property for real time applications. The purpose of this paper is to complete the classical stability analysis of the Kalman filter for general time varying systems. A proof of the stability of the one step ahead predictor, which is embedded in the Kalman filter, is presented in this paper, whereas the classical results were focused on the stability of the filter. The predictor stability is particularly important for linear parameter varying (LPV) system identification by means of prediction error minimisation.