scholarly journals A Valid Dynamical Control on the Reverse Osmosis System Using the CESTAC Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 48
Author(s):  
Samad Noeiaghdam ◽  
Denis Sidorov ◽  
Alyona Zamyshlyaeva ◽  
Aleksandr Tynda ◽  
Aliona Dreglea
Keyword(s):  
Reverse Osmosis ◽  
Numerical Procedure ◽  
Optimal Solution ◽  
Absolute Error ◽  
Optimal Approximation ◽  
Successive Approximations ◽  
Mathematical Methods ◽  
Optimal Error ◽  
Integration Rule ◽  
Cestac Method

The aim of this study is to present a novel method to find the optimal solution of the reverse osmosis (RO) system. We apply the Sinc integration rule with single exponential (SE) and double exponential (DE) decays to find the approximate solution of the RO. Moreover, we introduce the stochastic arithmetic (SA), the CESTAC method (Controle et Estimation Stochastique des Arrondis de Calculs) and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library instead of the mathematical methods based on the floating point arithmetic (FPA). Applying this technique, we would be able to find the optimal approximation, the optimal error and the optimal iteration of the method. The main theorems are proved to support the method analytically. Based on these theorems, we can apply a new stopping condition in the numerical procedure instead of the traditional absolute error. These theorems show that the number of common significant digits (NCSDs) of exact and approximate solutions are almost equal to the NCSDs of two successive approximations. The numerical results are obtained for both SE and DE Sinc integration rules based on the FPA and the SA. Moreover, the number of iterations for various ε are computed in the FPA. Clearly, the DE case is more accurate and faster than the SE for finding the optimal approximation, the optimal error and the optimal iteration of the RO system.

scholarly journals Advantages of the Discrete Stochastic Arithmetic to Validate the Results of the Taylor Expansion Method to Solve the Generalized Abel’s Integral Equation

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1370
Author(s):  
Eisa Zarei ◽  
Samad Noeiaghdam
Keyword(s):  
Integral Equation ◽  
Taylor Expansion ◽  
Expansion Method ◽  
Absolute Error ◽  
Optimal Error ◽  
Cestac Method ◽  
Stochastic Arithmetic ◽  
Cadna Library ◽  
Numerical Instabilities ◽  
Termination Criterion

The aim of this paper is to apply the Taylor expansion method to solve the first and second kinds Volterra integral equations with Abel kernel. This study focuses on two main arithmetics: the FPA and the DSA. In order to apply the DSA, we use the CESTAC method and the CADNA library. Using this method, we can find the optimal step of the method, the optimal approximation, the optimal error, and some of numerical instabilities. They are the main novelties of the DSA in comparison with the FPA. The error analysis of the method is proved. Furthermore, the main theorem of the CESTAC method is presented. Using this theorem we can apply a new termination criterion instead of the traditional absolute error. Several examples are approximated based on the FPA and the DSA. The numerical results show the applications and advantages of the DSA than the FPA.

scholarly journals Size optimization of a hybrid PV/wind/diesel/battery power system for reverse osmosis desalination

2019 ◽  
Vol 9 (4) ◽  
pp. 405-422 ◽  
Author(s):  
Daming Xu ◽  
Tom Acker ◽  
Xuhui Zhang
Keyword(s):  
Reverse Osmosis ◽  
Optimal Solution ◽  
Energy System ◽  
Optimal Configuration ◽  
Nonlinear Integer Programming ◽  
Sensitivity Analyses ◽  
Diesel Generator ◽  
Battery System ◽  
Photovoltaic Panel ◽  
Levelized Cost

Abstract This study was to find the optimal configuration for an independent renewable energy system for reverse osmosis (RO) desalination. The objective was to find the lowest levelized cost of energy (LCOE), with power reliability as the constraint. A genetic algorithm was used to solve the nonlinear integer programming program. A site with brackish groundwater in Arizona, USA was selected. The capacity of the RO system was 18.93 m3/d (5,000 gal/d), requiring a constant power consumption of 3.95 kW. Two scenarios were considered in terms of diesel generator (DG) allowed running time. The results showed that the optimal configuration was a hybrid photovoltaic/wind/diesel/battery system with 0.56 USD/kWh and the corresponding levelized cost of water 3.84 USD/m3, when the DG can run in any hour every day. The optimal solution was a hybrid wind/photovoltaic/battery system with 0.69 USD/kWh and 4.48 USD/m3, when the DG can run between 9 am and 9 pm every day for noise control. Both the two LCOWs were about half of the 7.9 USD/m3 currently paid by residents that live in the area. Sensitivity analyses showed the LCOE was fairly insensitive to photovoltaic panel tilt angle over a range for both the two configurations.

Joint reliability based design and periodic preventive maintenance policy for systems sold with warranty

2016 ◽  
Vol 22 (1) ◽  
pp. 2-17 ◽  
Author(s):  
M.N. Darghouth ◽  
Daoud Ait-Kadi ◽  
Anis Chelbi
Keyword(s):  
Average Cost ◽  
Numerical Procedure ◽  
Optimal Solution ◽  
Design Stage ◽  
Maintenance Policy ◽  
Content Type ◽  
Warranty Period ◽  
Reliability Based Design ◽  
Total Average Cost ◽  
Total Average

Purpose – The authors consider a system which is a part of a complex equipment (e.g. aircraft, automobile, medical equipment, production machine, etc.), and which consists of N independent series subsystems. The purpose of this paper is to determine simultaneously the system design (reliability) and its preventive maintenance (PM) replacements periodicity which minimize the total average cost per time unit over the equipment useful life, taking into account a minimum required reliability level between consecutive replacements. Design/methodology/approach – The problem is tackled in the context of reliability-based design (RBD) considering at the same time the burn-in of components, the warranty commitment and the maintenance strategy to be adopted. A mathematical model is developed to express the total average cost per time unit to be minimized under a reliability constraint. The total average cost includes the cost of acquiring and assembling components, the burn-in of each component, preventive and corrective replacements performed during the warranty and post-warranty periods. A numerical procedure is proposed to solve the problem. Findings – For any given set of input data including components reliability, their cost and the costs of their preventive and corrective replacements, the system design (reliability) and the periodicity of preventive replacement during the post-warranty period is obtained such as the system’s total average cost per time unit is minimized. The obtained results clearly indicate that a decrease in the number of PM actions to be performed during the post-warranty period increases the number of components to be added at each subsystem at the design stage. Research limitations/implications – Given that the objective function (cost rate function) to be minimized is non-linear and involves several integer variables, it has not been possible to derive the optimal solution. A numerical procedure based on a heuristic approach has been proposed to solve the problem finding a nearly optimal solution for a given set of input data. Practical implications – This paper offers to manufacturers a comprehensive approach to look for the most economical combination of the reliability level to be given to their products at the design stage, on one hand, and the PM policy to be adopted, on the other hand, given the offered warranty and service for the products and reliability requirements during the life cycle. Originality/value – While the RBD problem has been largely treated, most of the published works have focussed on the development or the improvement of solving techniques used to find the optimal configuration. In this paper the authors provide a more comprehensive approach that considers simultaneously RBD, the burn-in and warranty periods, along with the maintenance policy to be adopted. The authors also consider the context of products whose component failures cannot be rectified through repair actions. They can only be fixed by replacement.

Evaluation of Slug Flow-Induced Flexural Loading in Pipelines Using a Surrogate Model

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Ibrahim A. Sultan ◽  
Ahmed M. Reda ◽  
Gareth L. Forbes
Keyword(s):  
Surrogate Model ◽  
Slug Flow ◽  
Stochastic Perturbation ◽  
Numerical Procedure ◽  
Bending Moment ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Successive Approximations ◽  
Worked Example ◽  
Form Model

Slug flow induces vibration in pipelines, which may, in some cases, result in fatigue failure. This can result from dynamic stresses, induced by the deflection and bending moment in the pipe span, growing to levels above the endurance limits of the pipeline material. As such, it is of paramount importance to understand and quantify the size of the pipeline response to slug flow under given speed and damping conditions. This paper utilizes the results of an optimization procedure to devise a surrogate closed-form model, which can be employed to calculate the maximum values of the pipeline loadings at given values of speed and damping parameters. The surrogate model is intended to replace the computationally costly numerical procedure needed for the analysis. The maximum values of the lateral deflection and bending moment, along with their locations, have been calculated using the optimization method of stochastic perturbation and successive approximations (SPSA). The accuracy of the proposed surrogate model will be validated numerically, and the model will be subsequently used in a numerical example to demonstrate its applicability in industrial situations. An accompanying spreadsheet with this worked example is also given.

scholarly journals Forecasting the cost of the means of measuring

2018 ◽  
Vol 28 (4) ◽  
pp. 76-84
Author(s):  
R. S. Anosov ◽  
D. M. Byvshikh ◽  
S. G. Zelenskaya
Keyword(s):  
Optimal Solution ◽  
Electronic Equipment ◽  
Measuring Instruments ◽  
Mathematical Methods ◽  
High Frequency Signal ◽  
Electronic Measuring ◽  
Urgent Task ◽  
Forecast Models ◽  
Multiplicative Models ◽  
The Cost

The cost of electronic measuring instruments is influenced by their technical characteristics and design factors. Moreover, this influence is often complex non-linear in nature, which greatly complicates the construction of an adequate cost forecast. When justifying the composition of complex measuring systems, the error can be significant and lead to a non- optimal solution. Therefore, improving the quality of forecasts of measuring instruments cost, that are part of the system for testing special-purpose electronic equipment is an urgent task, which is considered in the presented article. When considering the main approaches to forecasting measuring instruments cost, the apparatus of economic and mathematical methods is applied: mathematical statistics, qualitative analysis of the main characteristics and factors determining the measuring instruments cost, comparative analysis of the technical level of radio-electronic equipment samples, and the analog method. As an example, additive and multiplicative models are considered for practical calculations of the cost of high-frequency signal generators and spectrum analyzers as a function of the technical characteristics of these devices. Corrective functions have been identified, the use of which significantly improves the accuracy of forecast, which proves the feasibility of using such functions in forecast models of the measuring equipment cost.

scholarly journals INDEX INSURANCE DESIGN

2019 ◽  
Vol 49 (2) ◽  
pp. 491-523
Author(s):  
Jinggong Zhang ◽  
Ken Seng Tan ◽  
Chengguo Weng
Keyword(s):  
Numerical Procedure ◽  
Optimal Solution ◽  
Utility Functions ◽  
Index Insurance ◽  
Linear Type ◽  
Weather Index ◽  
Basis Risk ◽  
Temperature And Precipitation ◽  
General Utility ◽  
Highly Nonlinear

AbstractIn this article, we study the problem of optimal index insurance design under an expected utility maximization framework. For general utility functions, we formally prove the existence and uniqueness of optimal contract and develop an effective numerical procedure to derive the optimal solution. For exponential utility and quadratic utility functions, we obtain analytical expression of the optimal indemnity function. Our results show that the indemnity can be a highly nonlinear and even non-monotonic function of the index variable in order to align with the actual loss variable so as to achieve the best reduction in basis risk. Due to the generality of model setup, our proposed method is readily applicable to a variety of insurance applications including index-linked mortality securities, weather index agriculture insurance, and index-based catastrophe insurance. Our method is illustrated by numerical examples where weather index insurance is designed for protection against the adverse rice yield using temperature and precipitation as the underlying indices. Numerical results show that our optimal index insurance significantly outperforms linear-type index insurance contracts in terms of basis risk reduction.

Ensemble-Based Data Assimilation of volcanic ash clouds from satellite observations: application to the 24 December 2018 Mt.Etna explosive eruption.

2021 ◽  
Author(s):  
Federica Pardini ◽  
Stefano Corradini ◽  
Antonio Costa ◽  
Lorenzo Guerrieri ◽  
Tomaso Esposti Ongaro ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Kalman Filters ◽  
Volcanic Ash ◽  
Explosive Eruption ◽  
Numerical Models ◽  
Numerical Procedure ◽  
Optimal Solution ◽  
Volcanic Eruptions ◽  
Satellite Observations ◽  
Mt Etna

<p>Explosive volcanic eruptions release high amounts of ash into the atmosphere. Accurate tracking and forecasting of ash dispersal into the atmosphere and quantification of its uncertainty is of fundamental importance for volcanic hazard mitigation. Numerical models represent a powerful tool to monitor ash clouds in real-time, but limits and uncertainties affect numerical results. A way to improve numerical forecasts is by assimilating satellite observations of ash clouds through Data Assimilation algorithms, such as Ensemble-based Kalman Filters. In this study, we present the implementation of the so-called Local Ensemble Transform Kalman Filters inside a numerical procedure which simulates the release and transport of volcanic ash during explosive eruptions. The numerical procedure consists of the eruptive column model PLUME-MoM coupled with the tephra transport and dispersal model HYSPLIT. When satellite observations are available, ash maps supplied by PLUME-MoM/HYSPLIT are sequentially corrected/modified using ash column loading as retrieved from space. The new volcanic ash state represents the optimal solution with minimized uncertainties with respect to numerical estimates and observations. To test the Data Assimilation procedure, we used satellite observations of the volcanic cloud released during the explosive eruption that occurred at Mt. Etna (Italy) on 24 December 2018. Satellite observations have been carried out by the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) instrument, on board the Meteosat Second Generation (MSG) geostationary satellite. Results show that the assimilation procedure significantly improves the current ash state and the forecast. In addition, numerical tests show that the use of sequential Kalman Filters does not require a precise initialization of the numerical model, being able to improve the forecasts as the assimilation cycles are performed.</p>

Multiobjective Optimization of Multiloop Fractional Order PID Controller Tuned Using Bat Algorithm for Two Interacting Conical Tank Process

2014 ◽  
Vol 704 ◽  
pp. 373-379
Author(s):  
S.K. Lakshmanaprabu ◽  
U. Sabura Banu
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Controller Design ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Bat Algorithm ◽  
Absolute Error ◽  
Fractional Order Pid ◽  
Fractional Order Pid Controller

Multiloop fractional order PID controller is tuned using Bat algorithm for two interacting conical tank process. Two interacting conical tank process is modelled using mass balance equations. Two Interacting Conical Tank process is a complex system involving tedious interaction. Straight forward multiloop PID controller design involves various steps to design the controller. Due to easy implementation and quick convergence, Bat algorithm is used in recent past for solving continuous non-linear optimization problems to achieve global optimal solution. Bat algorithm, a swarm intelligence technique will be attempted to tune the multiloop fractional order PID controller for two interacting conical tank process. The multi objective optimized multiloop fractional PID controller is tested for tracking, disturbance rejection for minimum Integral time absolute error.

scholarly journals A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1321
Author(s):  
Samad Noeiaghdam ◽  
Sanda Micula ◽  
Juan J. Nieto
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Order ◽  
Point Theorem ◽  
Successive Approximations ◽  
Banach Fixed Point Theorem ◽  
Order Model ◽  
Existence Of A Solution ◽  
Cestac Method ◽  
Fractional Order Model

In this paper, a nonlinear fractional order model of COVID-19 is approximated. For this aim, at first we apply the Caputo–Fabrizio fractional derivative to model the usual form of the phenomenon. In order to show the existence of a solution, the Banach fixed point theorem and the Picard–Lindelof approach are used. Additionally, the stability analysis is discussed using the fixed point theorem. The model is approximated based on Indian data and using the homotopy analysis transform method (HATM), which is among the most famous, flexible and applicable semi-analytical methods. After that, the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library, which are based on discrete stochastic arithmetic (DSA), are applied to validate the numerical results of the HATM. Additionally, the stopping condition in the numerical algorithm is based on two successive approximations and the main theorem of the CESTAC method can aid us analytically to apply the new terminations criterion instead of the usual absolute error that we use in the floating-point arithmetic (FPA). Finding the optimal approximations and the optimal iteration of the HATM to solve the nonlinear fractional order model of COVID-19 are the main novelties of this study.

scholarly journals Modified election algorithm in hopfield neural network for optimal random k satisfiability representation

2020 ◽  
Vol 11 ◽  
pp. 16
Author(s):  
Hamza Abubakar ◽  
Shamsul Rijal Muhammad Sabri ◽  
Sagir Abdu Masanawa ◽  
Surajo Yusuf
Keyword(s):  
Neural Network ◽  
Mean Absolute Error ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Information Criterion ◽  
Hopfield Neural Network ◽  
Absolute Error ◽  
Current Standard ◽  
Election Algorithm ◽  
Logical Representation

Election algorithm (EA) is a novel metaheuristics optimization model motivated by phenomena of the socio-political mechanism of presidential election conducted in many countries. The capability and robustness EA in finding an optimal solution to optimization has been proven by various researchers. In this paper, modified version of EA has been utilized in accelerating the searching capacity of Hopfield neural network (HNN) learning phase for optimal random-kSAT logical representation (HNN-R2SATEA). The utility of the proposed approach has been contrasted with the current standard exhaustive search algorithm (HNN-R2SATES) and the newly developed algorithm HNN-R2SATICA. From the analysis obtained, it has been clearly shown that the proposed hybrid computational model HNN-R2SATEA outperformed other existing model in terms of global minima ratio (Zm), mean absolute error (MAE), Bayesian information criterion (BIC) and execution time (ET). The finding portrays that the MEA algorithm surpassed the other two algorithms for optimal random-kSAT logical representation.

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