Search results for: distribution function bootstrap control limit

Authors: Al Omari Mohammed Ahmed

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This paper focuses on Maximum Likelihood Estimator with Covariate. Covariates are incorporated into the Weibull model. Under this regression model with regards to maximum likelihood estimator, the parameters of the covariate, shape parameter, survival function and hazard rate of the Weibull regression distribution with right censored data are estimated. The mean square error (MSE) and absolute bias are used to compare the performance of Weibull regression distribution. For the simulation comparison, the study used various sample sizes and several specific values of the Weibull shape parameter.

Keywords: weibull regression distribution, maximum likelihood estimator, survival function, hazard rate, right censoring

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Authors: Slobodan B. Tričković

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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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Authors: Syeda Qamarunnisa, Ishrat Jamil, Abid Azhar, Zabta K. Shinwari, Syed Irtifaq Ali

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A phylogenetic analysis of family Solanaceae was conducted using sequence data from the chloroplast intergenic atpB-rbcL spacer. Sequence data was generated from 17 species representing 09 out of 14 genera of Solanaceae from Pakistan. Cladogram was constructed using maximum parsimony method and results indicate that Solanaceae is mainly divided into two subfamilies; Solanoideae and Cestroideae. Four major clades within Solanoideae represent tribes; Physaleae, Capsiceae, Datureae and Solaneae are supported by high bootstrap value and the relationships among them are not corroborating with the previous studies. The findings established that subfamily Cestroideae comprised of three genera; Cestrum, Lycium, and Nicotiana with high bootstrap support. Position of Nicotiana inferred with atpB-rbcL sequence is congruent with traditional classification, which placed the taxa in Cestroideae. In the current study Lycium unexpectedly nested with Nicotiana with 100% bootstrap support and identified as a member of tribe Nicotianeae. Expanded sampling of other genera from Pakistan could be valuable towards improving our understanding of intrafamilial relationships within Solanaceae.

Keywords: systematics, solanaceae, phylogenetics, intergenic spacer, tribes

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Authors: Nasser Mohamed Ramli, Mohamad Syafiq Mohamad

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Many types of controllers were applied on the continuous stirred tank reactor (CSTR) unit to control the temperature. In this research paper, Proportional-Integral-Derivative (PID) controller are compared with Fuzzy Logic controller for temperature control of CSTR. The control system for temperature non-isothermal of a CSTR will produce a stable response curve to its set point temperature. A mathematical model of a CSTR using the most general operating condition was developed through a set of differential equations into S-function using MATLAB. The reactor model and S-function are developed using m.file. After developing the S-function of CSTR model, User-Defined functions are used to link to SIMULINK file. Results that are obtained from simulation and temperature control were better when using Fuzzy logic control compared to PID control.

Keywords: CSTR, temperature, PID, fuzzy logic

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Authors: Qasim Kriri, Harsh B. Desai

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Water supply and sanitation in Saudi Arabia is portrayed by difficulties and accomplishments. One of the fundamental difficulties is water shortage. With a specific end goal to beat water shortage, significant ventures have been attempted in sea water desalination, water circulation, sewerage, and wastewater treatment. The motivation behind Statistical Process Control (SPC) is to decide whether the execution of a procedure is keeping up an acceptable quality level [AQL]. SPC is an analytical decision-making method. A fundamental apparatus in the SPC is the Control Charts, which follow the inconstancy in the estimations of the item quality attributes. By utilizing the suitable outline, administration can decide whether changes should be made with a specific end goal to keep the procedure in charge. The two most important quality factors in the distilled water which were taken into consideration were pH (Potential of Hydrogen) and TDS (Total Dissolved Solids). There were three stages at which the quality checks were done. The stages were as follows: (1) Water at the source, (2) water after chemical treatment & (3) water which is sent for packing. The upper specification limit, central limit and lower specification limit are taken as per Saudi water standards. The procedure capacity to accomplish the particulars set for the quality attributes of Berain water Factory chose to be focused by the proposed SPC system.

Keywords: acceptable quality level, statistical quality control, control charts, process charts

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Authors: Citra Pertiwi, Muhammad Fikruzzaman Rahawarin

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Government of Indonesia had committed to increasing its national defense the budget up to 1,5 percent of GDP. However, the budget increase does not necessarily allocate efficiently and effectively. Using Data Envelopment Analysis (DEA), the operational units of Indonesian Armed Forces are considered as a proxy to measure those two aspects. The bootstrap technique is being used as well to reduce uncertainty in the estimation. Additionally, technological change is being measured as a nonstationary component. Nearly half of the units are being estimated as fully efficient, with less than a third is considered as effective. Longer and larger sets of data might increase the robustness of the estimation in the future.

Keywords: bootstrap, effectiveness, efficiency, DEA, military, Malmquist, technological change

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Authors: Encarnación Álvarez-Verdejo, Raúl Amor-Pulido, Pablo J. Moya-Fernández, Juan F. Muñoz-Rosas, Francisco J. Blanco-Encomienda

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Many companies use the statistical tool named as statistical quality control, and which can have a high cost for the companies interested on these statistical tools. The evaluation of the quality of products and services is an important topic, but the reduction of the cost of the implantation of the statistical quality control also has important benefits for the companies. For this reason, it is important to implement a economic design for the various steps included into the statistical quality control. In this paper, we describe some relevant aspects related to the economic design of a quality control chart for the proportion of defective items. They are very important because the suggested issues can reduce the cost of implementing a quality control chart for the proportion of defective items. Note that the main purpose of this chart is to evaluate and control the proportion of defective items of a production process.

Keywords: proportion, type I error, economic plan, distribution function

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Authors: Mustafa Sahin, İlkay Yavrucuk

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This paper presents a wind turbine envelope protection control algorithm that protects Variable Speed Variable Pitch (VSVP) wind turbines from damage during operation throughout their below and above rated regions, i.e. from cut-in to cut-out wind speed. The proposed approach uses a neural network that can adapt to turbines and their operating points. An algorithm monitors instantaneous wind and turbine states, predicts a wind speed that would push the turbine to a pre-defined envelope limit and, when necessary, realizes an avoidance action. Simulations are realized using the MS Bladed Wind Turbine Simulation Model for the NREL 5 MW wind turbine equipped with baseline controllers. In all simulations, through the proposed algorithm, it is observed that the turbine operates safely within the allowable limit throughout the below and above rated regions. Two example cases, adaptations to turbine operating points for the below and above rated regions and protections are investigated in simulations to show the capability of the proposed envelope protection system (EPS) algorithm, which reduces excessive wind turbine loads and expectedly increases the turbine service life.

Keywords: adaptive envelope protection control, limit detection and avoidance, neural networks, ultimate load reduction, wind turbine power control

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Authors: S. H. Arnaud Kanga, O. Hili, S. Dabo-Niang

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Spatial prediction is an issue appealing and attracting several fields such as agriculture, environmental sciences, ecology, econometrics, and many others. Although multiple non-parametric prediction methods exist for spatial data, those are based on the conditional expectation. This paper took a different approach by examining a non-parametric spatial predictor of the conditional quantile. The study especially observes the stationary multidimensional spatial process over a rectangular domain. Indeed, the proposed quantile is obtained by inverting the conditional distribution function. Furthermore, the proposed estimator of the conditional distribution function depends on three kernels, where one of them controls the distance between spatial locations, while the other two control the distance between observations. In addition, the almost complete convergence and the convergence in mean order q of the kernel predictor are obtained when the sample considered is alpha-mixing. Such approach of the prediction method gives the advantage of accuracy as it overcomes sensitivity to extreme and outliers values.

Keywords: conditional quantile, kernel, nonparametric, stationary

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Authors: Mouad Zouina, Benaceur Outtaj

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The proposed work falls within the context of improving data security for m-commerce systems. In this context we have placed under the light some flaws encountered in HTTPS the most used m-commerce protocol, particularly the man in the middle attack, shortly MITM. The man in the middle attack is an active listening attack. The idea of this attack is to target the handshake phase of the HTTPS protocol which is the transition from a non-secure connection to a secure connection in our case HTTP to HTTPS. This paper proposes a solution to fix those flaws based on the upgrade of HSTS standard handshake sequence using the DNSSEC standard.

Keywords: m-commerce, HTTPS, HSTS, DNSSEC, MITM bootstrap vulnerability

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Authors: Hooman Dabirmanesh, Attila M. Zsaki

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Traditionally, rock slope stability is carried out using limit equilibrium analysis when investigating toppling failure. In these equilibrium methods, internal forces exerted between columns are not clearly defined, and to the authors’ best knowledge, there is no consensus in literature with respect to the results of analysis. A discrete element method-based numerical model was developed and applied to simulate the behavior of rock layers subjected to toppling failure. Based on this calibrated numerical model, a study of the location and distribution of internal forces that result in equilibrium was carried out. The sum of side forces was applied at a point on a block which properly represents the force to determine the inter-column force distribution. In terms of the side force distribution coefficient, the result was compared to those obtained from laboratory centrifuge tests. The results of the simulation show the suitable criteria to select the correct position for the internal exerted force between rock layers. In addition, the numerical method demonstrates how a theoretical method could be reliable by considering the interaction between the rock layers.

Keywords: contact bond, discrete element, force distribution, limit equilibrium, tensile stress

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Authors: Ramin Rostamkhani, Thurasamy Ramayah

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One of the most important topics of today’s industrial organizations is the challenging issue of supply chain management. In this field, scientists and researchers have published numerous practical articles and models, especially in the last decade. In this research, to our best knowledge, the discussion of data modeling of supply chain management components using well-known statistical distribution functions has been considered. The world of science owns mathematics, and showing the behavior of supply chain data based on the characteristics of statistical distribution functions is innovative research that has not been published anywhere until the moment of doing this research. In an analytical process, describing different aspects of functions including probability density, cumulative distribution, reliability, and failure function can reach the suitable statistical distribution function for each of the components of the supply chain management. It can be applied to predict the behavior data of the relevant component in the future. Providing a model to adapt the best statistical distribution function in the supply chain management components will be a big revolution in the field of the behavior of the supply chain management elements in today's industrial organizations. Demonstrating the final results of the proposed model by introducing the process capability indices before and after implementing it alongside verifying the approach through the relevant assessment as an acceptable verification is a final step. The introduced approach can save the required time and cost to achieve the organizational goals. Moreover, it can increase added value in the organization.

Keywords: analyzing, process capability indices, statistical distribution functions, supply chain management components

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Authors: Zubier Arfan, Paul Johnson

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The electronification of financial markets and the rise of algorithmic trading has sparked a lot of interest from the mathematical community, for the market making-problem in particular. The research presented in this short paper solves the classic stochastic control problem in order to derive the strategy for a market-maker. It also shows how to calibrate and simulate the strategy with real limit order book data for back-testing. The ambiguity of limit-order priority in back-testing is dealt with by considering optimistic and pessimistic priority scenarios. The model, although it does outperform a naive strategy, assumes constant volatility, therefore, is not best suited to the LOB data. The Heston model is introduced to describe the price and variance process of the asset. The Trader's constant absolute risk aversion utility function is optimised by numerically solving a 3-dimensional Hamilton-Jacobi-Bellman partial differential equation to find the optimal limit order quotes. The results show that the stochastic volatility market-making model is more suitable for a risk-averse trader and is also less sensitive to calibration error than the constant volatility model.

Keywords: market-making, market-microsctrucure, stochastic volatility, quantitative trading

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Authors: Veronica Diaz Quezada

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The society of the 21st century requires training of engineers capable of solving routine and non-routine problems in applications of the limit of real functions, as part of the course Calculus I. For this purpose, research was conducted with a methodological design that combines quantitative and qualitative procedures and that aims, to identify and to characterize the types of problems according to their nature and context, through the application of a mathematics test; to know— through a questionnaire— the opinion of difficulties in their solution, previous and missing knowledge of some students of three engineering careers of a state university in Chile. This research is completed with three case studies. The results favor the performance of students in solving problems of a fantasist and realistic context, but these do not guarantee mathematical skills which are necessary to solve non-routine problems of limit applications. In conclusion, through this research, it became clear that the students of the three engineerings do not have all the necessary skills to solve problems of application of the limit of a function of the real variable.

Keywords: case studies, engineering program, limits, problem solving

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Authors: Mohammed Qasim, Kyoung-Dae Kim

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In this paper, we present the design of the super-ellipsoidal potential function (SEPF), that can be used for autonomous collision avoidance of an unmanned aerial vehicle (UAV) in a 3-dimensional space. In the design of SEPF, we have the full control over the shape and size of the potential function. In particular, we can adjust the length, width, height, and the amount of flattening at the tips of the potential function so that the collision avoidance motion vector generated from the potential function can be adjusted accordingly. Based on the idea of the SEPF, we also propose an approach for the local autonomy of a UAV for its collision avoidance when the UAV is teleoperated by a human operator. In our proposed approach, a teleoperated UAV can not only avoid collision autonomously with other surrounding objects but also track the operator’s control input as closely as possible. As a result, an operator can always be in control of the UAV for his/her high-level guidance and navigation task without worrying too much about the UAVs collision avoidance while it is being teleoperated. The effectiveness of the proposed approach is demonstrated through a human-in-the-loop simulation of quadrotor UAV teleoperation using virtual robot experimentation platform (v-rep) and Matlab programs.

Keywords: artificial potential function, autonomous collision avoidance, teleoperation, quadrotor

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Authors: R. S. Sheu, H. Usman, M. S. Lawal

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Takagi-Sugeno (T-S) fuzzy model based control of a load frequency deviation in a single machine with limit nonlinearity on power coefficient is presented in the paper. Two T-S fuzzy rules with only rotor angle variable as input in the premise part, and linear state space models in the consequent part involving characteristic matrices determined from limits set on the power coefficient constant are formulated, state feedback control gains for closed loop control was determined from the formulated Linear Matrix Inequality (LMI) with eigenvalue optimization scheme for asymptotic and exponential stability (speed of esponse). Numerical evaluation of the closed loop object was carried out in Matlab. Simulation results generated of both the open and closed loop system showed the effectiveness of the control scheme in maintaining load frequency stability.

Keywords: T-S fuzzy model, state feedback control, linear matrix inequality (LMI), frequency deviation control

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Authors: Mohamed El Hachimi, Abdelhakim Ballouk, Ilyas Khelafa, Abdelaziz Mouhou

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Introduction: Type 1 diabetes occurs when beta cells are destroyed by the body's own immune system. Treatment of type 1 diabetes mellitus could be greatly improved by applying a closed-loop control strategy to insulin delivery, also known as an Artificial Pancreas (AP). Method: In this paper, we present a new formulation of the cost function for a Model Predictive Control (MPC) utilizing a technic which accelerates the speed of control of the AP and tackles the nonlinearity of the control problem via asymmetric objective functions. Finding: The finding of this work consists in a new Model Predictive Control algorithm that leads to good performances like decreasing the time of hyperglycaemia and avoiding hypoglycaemia. Conclusion: These performances are validated under in silico trials.

Keywords: artificial pancreas, control algorithm, biomedical control, MPC, objective function, nonlinearity

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Authors: Noppatee Sabpayakom, Somporn Sirisumrannukul

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Due to incentive policies to promote renewable energy and energy efficiency, high penetration levels of very small power producers (VSPP) located in distribution networks have imposed technical barriers and established new requirements for protection and control of the networks. Although VSPPs have economic and environmental benefit, they may introduce negative effects and cause several challenges on the issue of protection and control system. This paper presents comprehensive studies of possible impacts on control and protection systems based on real distribution systems located in a metropolitan area. A number of scenarios were examined primarily focusing on state of islanding, and un-disconnected VSPP during faults. It is shown that without proper measures to address the issues, the system would be unable to maintain its integrity of electricity power supply for disturbance incidents.

Keywords: control and protection systems, distributed generation, renewable energy, very small power producers

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Authors: João Pereira Dos Santos

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The uneven spatial distribution of start-ups and their respective survival may reflect comparative advantages resulting from the local institutional background. For the first time, we explore this idea using Data Envelopment Analysis (DEA) to assess relative efficiency of Portuguese municipalities in this specific context. We depart from the related literature where expenditure is perceived as a desirable input by choosing a measure of fiscal responsibility and infrastructural variables in the first stage. Comparing results for 2006 and 2010, we find that mean performance decreased substantially with 1) the effects of the Global Financial Crisis; 2) as municipal population increases and 3) as financial independence decreases. A second stage is then computed employing a double-bootstrap procedure to evaluate how the regional context outside the control of local authorities (e.g. demographic characteristics and political preferences) impacts on efficiency.

Keywords: entrepreneurship, political economy, public finance, accountability, crisis, efficiency, Portuguese municipalities

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Authors: Debasis Sengupta, Sudipta Das

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The class of life distributions with decreasing mean residual life (DMRL) is well known in the field of reliability modeling. It contains the IFR class of distributions and is contained in the NBUE class of distributions. While upper and lower bounds of the reliability distribution function of aging classes such as IFR, IFRA, NBU, NBUE, and HNBUE have discussed in the literature for a long time, there is no analogous result available for the DMRL class. We obtain the upper and lower bounds for the reliability function of the DMRL class in terms of first order finite moment. The lower bound is obtained by showing that for any fixed time, the minimization of the reliability function over the class of all DMRL distributions with a fixed mean is equivalent to its minimization over a smaller class of distribution with a special form. Optimization over this restricted set can be made algebraically. Likewise, the maximization of the reliability function over the class of all DMRL distributions with a fixed mean turns out to be a parametric optimization problem over the class of DMRL distributions of a special form. The constructive proofs also establish that both the upper and lower bounds are sharp. Further, the DMRL upper bound coincides with the HNBUE upper bound and the lower bound coincides with the IFR lower bound. We also prove that a pair of sharp upper and lower bounds for the reliability function when the distribution is increasing mean residual life (IMRL) with a fixed mean. This result is proved in a similar way. These inequalities fill a long-standing void in the literature of the life distribution modeling.

Keywords: DMRL, IMRL, reliability bounds, hazard functions

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Authors: Eshwara Prasad Koorapati, R. Raman Goud, Swadesh Kumar Singh

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In the present work forming limit diagrams and strain distribution profile diagrams for extra deep drawing steel at room and elevated temperatures have been determined experimentally by conducting stretch forming experiments by using designed and fabricated warm stretch forming tooling setup. With the help of forming Limit Diagrams (FLDs) and strain distribution profile diagrams the formability of Extra Deep Drawing steel has been analyzed and co-related with mechanical properties like strain hardening coefficient (n) and normal anisotropy (r−).Mechanical properties of EDD steel from room temperature to 4500 C were determined and discussed the impact of temperature on the properties like work hardening exponent (n) anisotropy (r-) and strength coefficient of the material. Also, the fractured surfaces after stretching have undergone the some metallurgical investigations and attempt has been made to co-relate with the formability of EDD steel sheets. They are co-related and good agreement with FLDs at various temperatures.

Keywords: FLD, micro hardness, strain distribution profile, stretch forming

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Authors: M. Movahedi Rad

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In this study, a general approach to the reliability based limit analysis of laterally loaded piles is presented. In engineering practice, the uncertainties play a very important role. The aim of this study is to evaluate the lateral load capacity of free head and fixed-head long pile when the plastic limit analysis is considered. In addition to the plastic limit analysis to control the plastic behaviour of the structure, uncertain bound on the complementary strain energy of the residual forces is also applied. This bound has a significant effect for the load parameter. The solution to reliability-based problems is obtained by a computer program which is governed by the reliability index calculation.

Keywords: reliability, laterally loaded pile, residual strain energy, probability, limit analysis

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Authors: Tomoaki Hashimoto

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In recent decades, probabilistic constrained optimal control problems have attracted much attention in many research field. Although probabilistic constraints are generally intractable in an optimization problem, several tractable methods haven been proposed to handle probabilistic constraints. In most methods, probabilistic constraints are reduced to deterministic constraints that are tractable in an optimization problem. However, there is a gap between the transformed deterministic constraints in case of known and unknown probability distribution. This paper examines the conservativeness of probabilistic constrained optimization method with the unknown probability distribution. The objective of this paper is to provide a quantitative assessment of the conservatism for tractable constraints in probabilistic constrained optimization with the unknown probability distribution.

Keywords: optimal control, stochastic systems, discrete time systems, probabilistic constraints

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Authors: Vladimir S. Timofeev

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In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique, author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation

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Authors: Seon Soon Choi

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Magnesium alloy has been widely used in structure such as an automobile. It is necessary to consider probabilistic characteristics of a structural material because a fatigue behavior of a structure has a randomness and uncertainty. The purpose of this study is to find the characteristics of the cumulative distribution function (CDF) of the grown crack size at a specified fatigue crack propagation life and to investigate a statistical crack propagation in magnesium alloys. The statistical fatigue data of the grown crack size are obtained through the fatigue crack propagation (FCP) tests under different maximum fatigue load conditions conducted on the replicated specimens of magnesium alloys. The 3-parameter Weibull distribution is used to find the CDF of grown crack size. The CDF of grown crack size in case of larger maximum fatigue load has longer tail in below 10 percent and above 90 percent. The fatigue failure occurs easily as the tail of CDF of grown crack size becomes long. The fatigue behavior under the larger maximum fatigue load condition shows more rapid propagation and failure mode.

Keywords: cumulative distribution function, fatigue crack propagation, grown crack size, magnesium alloys, maximum fatigue load

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Authors: S. Sudhharani

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Energy distribution networks are the main link between the energy industry and consumers and are subject to the most scrutiny and testing of any category. As a result, it is important to monitor energy levels during the distribution phase. Power distribution networks, on the other hand, remain subject to common problems, including voltage breakdown, power outages, harmonics, and capacitor switching, all of which disrupt sinusoidal waveforms and reduce the quality and power of the network. Using power appliances in the form of custom power appliances is one way to deal with energy quality issues. Dynamic Voltage Restorer (DVR), integrated with network and distribution networks, is one of these devices. At the same time, by injecting voltage into the system, it can adjust the voltage amplitude and phase in the network. In the form of injections and three-phase syncing, it is used to compensate for the difficulty of energy quality. This article examines the recent use of DVR for power compensation and provides data on the control of each DVR in distribution networks.

Keywords: dynamic voltage restorer (DVR), power quality, distribution networks, control systems(PWM)

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Authors: Amal Ezzidani, Abdelghani Ben Tahar, Mohamed Hanini

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A sequence of finite tandem queue is considered for this study. Each one has a single server, which operates under the egalitarian processor sharing discipline. External customers arrive at each queue according to a renewal input process and having a general service times distribution. Upon completing service, customers leave the current queue and enter to the next. Under mild assumptions, including critical data, we prove the existence and the uniqueness of the fluid solution. For asymptotic behavior, we provide necessary and sufficient conditions for the invariant state and the convergence to this invariant state. In the end, we establish the convergence of a correctly normalized state process to a fluid limit characterized by a system of algebraic and integral equations.

Keywords: fluid limit, fluid model, measure valued process, processor sharing, tandem queue

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Authors: Vibha Devi, Shabina Khanam

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Hemp (Cannabis sativa) possesses a rich content of ω-6 linoleic and ω-3 linolenic essential fatty acid in the ratio of 3:1, which is a rare and most desired ratio that enhances the quality of hemp oil. These components are beneficial for the development of cell and body growth, strengthen the immune system, possess anti-inflammatory action, lowering the risk of heart problem owing to its anti-clotting property and a remedy for arthritis and various disorders. The present study employs supercritical fluid extraction (SFE) approach on hemp seed at various conditions of parameters; temperature (40 - 80) °C, pressure (200 - 350) bar, flow rate (5 - 15) g/min, particle size (0.430 - 1.015) mm and amount of co-solvent (0 - 10) % of solvent flow rate through central composite design (CCD). CCD suggested 32 sets of experiments, which was carried out. As SFE process includes large number of variables, the present study recommends the application of resampling techniques for cross-validation of the obtained data. Cross-validation refits the model on each data to achieve the information regarding the error, variability, deviation etc. Bootstrap and jackknife are the most popular resampling techniques, which create a large number of data through resampling from the original dataset and analyze these data to check the validity of the obtained data. Jackknife resampling is based on the eliminating one observation from the original sample of size N without replacement. For jackknife resampling, the sample size is 31 (eliminating one observation), which is repeated by 32 times. Bootstrap is the frequently used statistical approach for estimating the sampling distribution of an estimator by resampling with replacement from the original sample. For bootstrap resampling, the sample size is 32, which was repeated by 100 times. Estimands for these resampling techniques are considered as mean, standard deviation, variation coefficient and standard error of the mean. For ω-6 linoleic acid concentration, mean value was approx. 58.5 for both resampling methods, which is the average (central value) of the sample mean of all data points. Similarly, for ω-3 linoleic acid concentration, mean was observed as 22.5 through both resampling. Variance exhibits the spread out of the data from its mean. Greater value of variance exhibits the large range of output data, which is 18 for ω-6 linoleic acid (ranging from 48.85 to 63.66 %) and 6 for ω-3 linoleic acid (ranging from 16.71 to 26.2 %). Further, low value of standard deviation (approx. 1 %), low standard error of the mean (< 0.8) and low variance coefficient (< 0.2) reflect the accuracy of the sample for prediction. All the estimator value of variance coefficients, standard deviation and standard error of the mean are found within the 95 % of confidence interval.

Keywords: resampling, supercritical fluid extraction, hemp oil, cross-validation

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Authors: Truong Nguyen Luan Vu, Le Hieu Giang, Le Linh

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The FOPI controller is proposed based on the main properties of the decoupling control scheme, as well as the fractional calculus. By using the simplified decoupling technique, the transfer function of decoupled apparent process is firstly separated into a set of n equivalent independent processes in terms of a ratio of the diagonal elements of original open-loop transfer function to those of dynamic relative gain array and the fraction – order PI controller is then developed for each control loops due to the Bode’s ideal transfer function that gives the desired fractional closed-loop response in the frequency domain. The simulation studies were carried out to evaluate the proposed design approach in a fair compared with the other existing methods in accordance with the structured singular value (SSV) theory that used to measure the robust stability of control systems under multiplicative output uncertainty. The simulation results indicate that the proposed method consistently performs well with fast and well-balanced closed-loop time responses.

Keywords: ideal transfer function of bode, fractional calculus, fractional order proportional integral (FOPI) controller, decoupling control system

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Authors: Zilaila Zakaria, Muhd Azri Abdul Razak, Muhammad Murtadha Othman, Mohd Ainor Yahya, Ismail Musirin, Mat Nasir Kari, Mohd Fazli Osman, Mohd Zaini Hassan, Baihaki Azraee

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Energy efficiency can be realized by minimizing the power loss with a sufficient amount of energy used in an electrical distribution system. In this report, a detailed analysis of the energy efficiency of an electric distribution system was carried out with an implementation of the optimal capacitor placement and sizing (OCPS). The particle swarm optimization (PSO) will be used to determine optimal location and sizing for the capacitors whereas energy consumption and power losses minimization will improve the energy efficiency. In addition, a certain number of busbars or locations are identified in advance before the PSO is performed to solve OCPS. In this case study, three techniques are performed for the pre-selection of busbar or locations which are the power-loss-index (PLI). The particle swarm optimization (PSO) is designed to provide a new population with improved sizing and location of capacitors. The total cost of power losses, energy consumption and capacitor installation are the components considered in the objective and fitness functions of the proposed optimization technique. Voltage magnitude limit, total harmonic distortion (THD) limit, power factor limit and capacitor size limit are the parameters considered as the constraints for the proposed of optimization technique. In this research, the proposed methodologies implemented in the MATLAB® software will transfer the information, execute the three-phase unbalanced load flow solution and retrieve then collect the results or data from the three-phase unbalanced electrical distribution systems modeled in the SIMULINK® software. Effectiveness of the proposed methods used to improve the energy efficiency has been verified through several case studies and the results are obtained from the test systems of IEEE 13-bus unbalanced electrical distribution system and also the practical electrical distribution system model of Sultan Salahuddin Abdul Aziz Shah (SSAAS) government building in Shah Alam, Selangor.

Keywords: particle swarm optimization, pre-determine of capacitor locations, optimal capacitors placement and sizing, unbalanced electrical distribution system

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