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This paper aims to propose an efficient and accurate method to analyse the transient heat conduction in a periodic structure with moving heat sources.

The moving heat source is modelled as a localised Gaussian distribution in space. Based on the spatial distribution, the physical feature of transient heat conduction and the periodic property of structure, a special feature of temperature responses caused by the moving heat source is illustrated. Then, combined with the superposition principle of linear system, within a small time-step, computation of results corresponding to the whole structure excited by the Gaussian heat source is transformed into that of some small-scale structures. Lastly, the precise integration method (PIM) is used to solve the temperature responses of each small-scale structure efficiently and accurately.

Within a reasonable time-step, the heat source applied on a unit cell can only cause the temperature responses of a limited number of adjacent unit cells. According to the above feature and the periodic property of a structure, the contributions caused by the moving heat source for the most of time-steps are repeatable, and the temperature responses of the entire periodic structure can be obtained by some small-scale structures.

A novel numerical method is proposed for analysing moving heat source problems, and the numerical examples demonstrate that the proposed method is much more efficient than the traditional methods, even for larger-scale problems and multiple moving heat source problems.

The purpose of this paper is to present research in detecting and identifying abrupt faults in controlled auto‐regressive (CAR) processes.

Model‐based approach is adopted in this paper. Two series of fault‐tolerant iterative estimators are set up to estimate online the coefficients in a CAR process. Based on these fault‐tolerant estimators, the detailed detecting and identifying algorithms are obtained for not only the pulse‐type faults but also the step‐type faults in CAR process.

This paper illustrates the useful information that can be obtained from residuals and that can be used to detect pulse‐type faults as well as step‐type faults. A fault‐tolerant recursive estimator for the coefficients of the CAR process is put forward. Using a simple transformation from step‐ to pulse‐type faults, all kinds of diagnosis methods to detect and identify step‐type faults can be used.

Fault‐tolerant estimators and fault detection and identification algorithms are aimed at abrupt faults in CAR processes.

Most of the algorithms given in this paper can be used in many different fields, such as process monitoring, safety control and change detection, etc.

This paper contributes to research of abrupt faults and abrupt changes in a CAR process and emphasizes identification of magnitudes of abrupt faults. The fault‐tolerant estimators are effective not only to detect faults but also to identify safely the coefficients CAR model.