Sirous Fathi Manesh

One of the main goals of reliability theory is to design systems with higher reliability. Among the methods of improving the reliability of a system, redundancy allocation means assigning one or more additional components to the system component or components. The different types of redundancy allocation are: active (hot) redundancy, cold standby redundancy and minimal repair redundancy. Although these allocations always increase the reliability of the system, a fundamental question is which component or components to apply redundancy to achieve a system with optimal reliability. In systems with dependent components, using the copula function theory, the lifetime of the system components and the dependence between them are modeled, and then, in terms of this dependence, the allocation of redundancy on the components has been investigated. Allocation of redundancy causes the change of the lifetime of the component to which the redundancy is assigned, the existence of this change has caused that in recent researches, the distortion function that is used in risk theory to model future risks is used to display The life span of the component can be used with redundancy or system allocation, and new and more general results have been obtained based on the shape of the distortion function. The effect of all the components is not the same during the lifetime of the system, and as a result, the allocation of redundancy does not have the same effect on all components, therefore the most effective component should be selected for the allocation of redundancy. In reliability, various measures are defined to measure the importance of the component, such as: Barlow-Proshan component importance measure and Birnbaum measure. Our main goal in this thesis is to find the optimal redundancy allocation by using common component importance measures and in systems with dependent components. For this purpose, the general framework of this thesis is proposed as follows: In the first chapter, we will explain the necessary introductions and definitions such as: concept of coherent system, structure function, concepts of aging, types of coherent systems, etc. An important tool in comparing the lifetime of systems is the theory of stochastic orderings, which we will discuss in this chapter. Among the other required concepts, there is the concept of copula function and distorsion function, which is expressed in a concise form. In the second chapter, we will introduce the Birnbaum measure and Barlow-Proshan component importance measure. We first define these measures for a system with independent components and then generalize these definitions for the dependent state. In the third chapter, we discuss the issue of redundancy allocation in a system with dependent components. In this chapter, we will first explain the concept of redundancy allocation and its types. And then we express results in the state of independence of the components and generalize them to the dependent state. In the fourth chapter, we examine the relationship between redundancy allocation and component importance measures for systems with dependent components. At the end, in the fifth chapter, we present the general conclusions about the conducted studies, and several suggestions for future studies are also presented.

Securing Industrial Internet of Things (IIoT) devices is critical due to the potentially devastating consequences of an attack. Machine learning (ML) and big data analytics are two powerful levers for analyzing and developing Internet of Things (IoT) technology. In this thesis, machine learning techniques are employed to design an intrusion detection system (IDS) in IoT networks. UNSW BoT-IoT dataset, developed in an Australian research institute in 2018, is adopted with the advantage of including multiclass well known cyber-attacks. Using feature extraction techniques, the number of features is decreased from 44 to 15 in order to reduce training time and complexity, an then train and test data sets are constituted with ratio of 80 to 20. Machine learning techniques decision tree (DT), random forest (RF), support vector machine (SVM), K-nearing neighborhood (KNN), and neural network (NN) are adopted to be trained and form the designed IDS. We have compared the performance through the same evaluation criteria to have a fair view of the effectiveness of the methods. Based on the results, RF and DT have demonstrated the best performance, considering the fact that DT has a low training time. Then, KNN⸲ SVM and ANN algorithms have shown better performance in the class respectively. It can be seen that these algorithms do not perform well in minority classes, which is not suitable for UNSW BoT-IoT dataset.

The correlation and relationship between two variables are fundamental concepts in statistics. Due to the importance of these concepts,various correlation coefficients have been defined to measure the intensity of dependency. Among the most common of them, Pearson, Spearman, and Tau Kendall correlation coefficients can be mentioned. These common correlation coefficients deal with the dependence between two variables in the whole domain. But, in some areas, the correlation between extreme values is much more important than the entire range. Therefore, it is necessary to define some coefficients to measure the intensity of correlation only in the extreme values. Tail dependence coefficients consider this issue. Because of the importance and application of these coefficients in various fields, this thesis discusses the definition of the tail correlation coefficient, its calculation, and its estimation methods. First, we state the definitions and concepts needed throughout the thesis, such as the copula function, concordance measure, the most common correlation coefficients, and tail dependence coefficients. Next, we express some essential theorems of the extreme values theory for the cases of one and two diminutions. We use them later to calculate and estimate the tail dependence coefficients. Then, parametric and semi-parametric methods of estimating tail dependence coefficients are studied under the conditions that either the random variables belong to elliptical distributions or the copula function are known. Finally, we study the non-parametric methods of estimation of the tail dependence coefficients.

‎Clustering is one of the important statistical tools in multivariate analysis in order to group and discover the hidden structures in the data‎. ‎In statistics‎, ‎clustering is often model-based‎, ‎meaning that the data are assumed to come from a Gaussian mixture model‎. ‎However‎, ‎Gaussian mixture models are usually not suitable for non-ellipsoidal data‎. ‎It also cannot model of the dependency structures in the data‎. ‎Copulas can be used to solve this problem‎. ‎The use of copulas in model-based clustering offers two direct advantages over current methods‎: ‎i) the appropriate choice of copulas provides the ability to obtain a range of exotic shapes for the clusters‎, ‎and ii) the explicit choice of marginal distributions for the clusters allows the modelling of multivariate data of various modes (either discrete or continuous) in a natural way‎. ‎To this end‎, ‎in the first chapter of this thesis‎, ‎the definition of clustering‎, ‎its importance‎, ‎applications and methods of clustering and copula function are defined‎. ‎In the second chapter‎, ‎we have discussed clustering based on the Gaussian mixture model in detail‎. ‎Furthermore in this chapter‎, ‎while defining the $MCLUS$T technique‎, ‎which is based on the decomposition of the variance-covariance matrix‎, ‎the method of estimating the parameters using the $EM$ algorithm is described from the theoretical and computational aspects‎. ‎In the third chapter‎, ‎the disadvantages of the model-based method in clustering data with heavy-tailed and tail dependence‎, ‎are stated‎, ‎and the use of the copula function to solve these problems is investigated‎. ‎Theoretical and computational methods using $IFM$ algorithms and $ECM$ algorithms to estimate parameters have also been described‎. ‎In addition‎, ‎by analyzing simulated and real examples‎, ‎the performance and accuracy increase in clustering based on the copula function model have been shown‎. ‎

امنیت و احراز هویت یک هدف اصلی در طراحی سیستم های محاسبات فعلی، از جمله سیستم های تعبیه شده، سیستم های سایبر فیزیکی و دستگاه های اینترنت اشیای صنعتی می باشد. با توجه به پیشرفت های روز افزون مبتنی بر حملات مخرب و کاهش امنیت تکنیک های تحمل پذیر خطا در اینترنت اشیاء، بکارگیری و ارائه روش هایی که بتوانند احراز هویت را در برابر حملات وارد بر شبکه نظیر حملات سایبری تضمین کرده و یا خطا را به حداقل برسانند، لازم و ضروری است. در این پژوهش به منظور افزایش دقت سیستم تشخیص نفوذ اینترنت اشیای صنعتی در برابر حملات سایبری، از روش ترکیبی مبتنی بر الگوریتم های فراابتکاری گرگ خاکستری‎ ‎ ( GWO ) و شبیه سازی تبرید‎ ‎ ( SA ) و الگوریتم های طبقه بندی DT، ANN و KNN استفاده شد. ابتدا داده های مربوط به حملات سایبری پس از مراحل پیش پردازش، نرمال سازی شد. در مرحله بعد با استفاده از الگوریتم های DT، ANN و KNN و ترکیب آن ها با الگوریتم های شبیه سازی تبرید و گرگ خاکستری، داده ها مورد آزمون و ارزیابی قرار گرفت. از مجموعه داده KDD Cup 99‎ برای ارزیابی مدل های پیشنهادی استفاده شده است. ‎ ‎بر مبنای نتایج بدست آمده مشخص گردید که استفاده از الگوریتم ترکیبی GWO-ANN با دقت 2273/93 درصد از نظر دقت در انتخاب ویژگی و همچنین میزان تشخیص حملات عملکرد بهتری دارد. همچنین می توان این مورد راه هم استنتاج کرد که الگوریتم ANN نسبت به الگوریتم های DT و KNN در تلفیق با الگوریتم های GWO و شبیه سازی تبرید دارای دقت بالاتری است. پس از الگوریتم ANN، الگوریتم درخت تصمیم ( DT ) در مرتبه دوم قرار می گیرد، و الگوریتمی که در تلفیق با دو الگوریتم GWO و SA دارای خطای محاسباتی بیشتری می باشد، الگوریتم KNN است. همچنین نتایج مقایسه ای ما با مقاله ای که از الگوریتم CFA استفاده کرده بیانگر آن است که روش پیشنهادی در مقایسه با روش CFA حدود 1763/1 درصد بهبود را نشان می دهد‎.‎

In the investment culture, risk is the potential investment loss that can be calculated. Therefore, identifying the types of risks and measuring them is very important. So far, various criteria have been proposed for measuring risk. The use of risk sizes such as value at risk (VaR) and conditional tail expectation (CTE) is common in the financial and in- surance markets. Estimation of these two risks is always one of the im- portant topics in insurance studies, so in recent years, appropriate and efficient methods for estimating these risks are very important. These methods use the empirical distribution function and the density kernel estimation method. On the other hand, comparing the size of risks in in- dependent and dependent portfolios is an important issue. To compare this size of risks in independent and dependent portfolios, we use nested L-statistics and compare the size of risks using a simulation study for different sample sizes and levels of significance.