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The rotating machines like gas turbine types are highly valuable in the gas transportation industry. They are often strategic and have a major impact on the proper operation of gas transport and compression facilities. In this context, the aim of this work is to increase efficiency and production by developing an approach for this kind of installations using real data collected from the operation of the gas turbine. The objective is to provide a database relating to the reliability, availability, and maintenance of gas turbines while using standard reliability approaches. In addition, ensuring maximum availability of this type of rotating machine by preventing its failures and reducing emissions, and by minimizing start-up sequences, which reduces emissions when starting this machine. Also, the proper operation of these gas turbine installations with the reliability approaches developed in this work makes it possible to model the effects of failures in order to predict optimal operating performance and increase the life of their components. This, therefore, ensures a reliable and safe operation of the gas turbine in a compression station for economically profitable gas recovery.

GARCH-MIDAS model of Engle et al. (2013) describes the volatility of daily returns as the product of a short-term volatility component, modelled by a Unit GARCH(1,1), and long-term component volatility which is modelled by a macroeconomic variable(s) which are observed at a lower frequency. This model has been applied extensively in volatility modelling using the Maximum Likelihood Estimation (MLE) Method despite that little is known about its finite sample properties. In this thesis, we fill this gap and extend it to other models such as EGARCH-MIDAS, and stochastic volatility models such as SVL-MIDAS and Heston-MIDAS models and their jump augmented versions to capture the leverage effect and the impact of rare events. Results of our first contribution indicate that in-sample and out-sample performance of GARCH type MIDAS models depend on the specification gt whereas τˆt is not sensitive to the choice of the short-term component of the volatility; our simulation and empirical studies suggest that whenever EGARCH(1,1), say, outperforms GARCH(1,1), EGARCH-MIDAS outperforms GARCH-MIDAS; and MLE estimate of GARCH-MIDAS, and EGARCH-MIDAS are not consistent when the returns series contain spikes or its volatility is highly persistent. These results led us to our second main contribution of estimating their parameters and those of their Jump augmented versions using Bayesian approach by overcoming the complexity of their posterior distributions by applying Metropolis Hasting simulation method. Our simulation and empirical studies indicate that our MCMC algorithms successfully capture the jump component and produce accurate estimates when MLE fails. Based on the findings of our first two contributions and the recognized out-performance of stochastic volatility models over GARCH type models, we developed SV-MIDAS, SVL-MIDAS, and Heston-MIDAS with their jump augmented extensions. Our MCMC algorithms can be extended to more complex multi-component volatility models to be considered in our future work.

Bearing fault diagnosis in induction motors under variable load and speed conditions remains a challenging task due to the complexity of fault‐induced transients in current signals. This study presents a novel deep learning‐based fault classification framework utilising Variational Mode Decomposition (VMD) for adaptive feature extraction and a Multi‐branch Convolutional Neural Network (1D‐MCNN) architecture for classification. The VMD hyperparameters were optimised based on kurtosis to ensure the extraction of the most informative Intrinsic Mode Functions (IMFs), significantly enhancing feature quality. Experimental validation under fixed, variable and noisy operating conditions demonstrated the superior performance of the proposed approach. The 1D‐CNN multi‐branch model consistently outperformed conventional artificial neural network (ANN) and single‐branch convolutional neural network (CNN) architectures, achieving 99.85% accuracy in fixed‐speed conditions and 99.75% in variable‐speed operations. Moreover, t‐SNE visualisations revealed improved class separability, confirming the robustness of the extracted features. These results highlight the efficacy of VMD‐guided deep learning architectures in accurately detecting bearing faults across diverse operational scenarios, reinforcing their potential for industrial predictive maintenance.

This study aims to examine the role of civil society in strengthening Algeria’s soft power by analyzing the model of the Tedjania order, as one of the most significant institutions of Algerian civil society. The Tedjania order possesses the capacity for internal and external adaptation and influence. The study also assesses the extent to which the Algerian state has successfully utilized it as a soft power resource contributing, domestically, to the preservation of national identity security and, externally, to the promotion of values of love, peace, and moderation.The research adopts Samuel Huntington’s framework to measure the institutional indicators of the Tedjania order—Algerian in origin and headquarters, yet global in its spread and influence—while also evaluating the degree of success achieved by the Algerian state in employing it as a source of soft power.The study concludes that Algeria has indeed begun adopting the strategic option of wisely employing the concept of soft power, particularly within African relations, by leveraging the Tedjania order as one of its resources. However, in terms of governance, development, and the structured management of soft power instruments, efforts remain relative and require improvement in the mechanisms employed.

This study aims to examine the role of civil society in strengthening Algeria's softpower by analyzing the model of the Tedjania order, as one of the most significant institutions of Algerian civil society. The Tedjania order possesses the capacity for internal and external adaptation and influence. The study also assesses the extent to which the Algerian state has successfully utilized it as a softpower resource contributing, domestically, to the preservation of national identity security and, externally, to the promotion of values of love, peace, and moderation. The research adopts Samuel Huntington's framework to measure the institutional indicators of the Tedjania order-Algerian in origin and headquarters, yet global in its spread and influencewhile also evaluating the degree of success achieved by the Algerian state in employing it as a source of softpower. The study concludes that Algeria has indeed begun adopting the strategic option of wisely employing the concept of softpower, particularly within African relations, by leveraging the Tedjania order as one of its resources. However, in terms of governance, development, and the structured management of softpower instruments, efforts remain relative and require improvement in the mechanisms employed.

The novel coronavirus disease (SARS-CoV-2) has caused many infections and deaths throughout the world; the spread of the coronavirus pandemic is still ongoing and continues to affect healthcare systems and economies of countries worldwide. Mathematical models are used in many applications for infectious diseases, including forecasting outbreaks and designing containment strategies. In this paper, we study two types of SIR and SEIR models for the coronavirus. This study focuses on the discrete-time and fractional-order of these models; we study the stability of the fixed points and orbits using the Jacobian matrix and the eigenvalues and eigenvectors of each case; moreover, we estimate the parameters of the two systems in fractional order. We present a statistical study of the coronavirus model in two countries: Saudi Arabia, which has successfully recovered from the SARS-CoV-2 pandemic, and China, where the number of infections remains significantly high.

This paper proposed a novel state estimation framework for nonlinear systems described by fractional-order (FO) and Takagi-Sugeno (TS) fuzzy models, targeting critical challenges associated with large modeling uncertainties. The key innovation was in the development of two complementary observer structures that estimated system states when premise variables were either measurable or non-measurable, and in the presence of unknown inputs and uncertain dynamics. The proposed methodology addressed uncertainties affecting system matrices, input matrices, and unknown input transmission matrices. It introduced a fractional-order Thau-Luenberger observer (FO-TLO) for systems with measurable premise variables, and a dedicated observer adapted to the case of non-measurable premise variables. Both configurations utilized Lyapunov-based stability theory and linear matrix inequality (LMI) methods to ensure robust, asymptotic, and theoretically guaranteed convergence of the state estimation error in the presence of time-varying and bounded uncertainties. The framework extended the observer design to a broader class of FO-TS systems, and it offered effective tools for fault diagnosis, system monitoring, and robust control in the presence of uncertain environments.