Search results for: an optimal error bound

Authors: Medine Demir, Volker John

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Fluid equations in a rotating frame of reference have a broad class of important applications in meteorology and oceanography, especially in the large-scale flows considered in ocean and atmosphere, as well as many physical and industrial applications. The Coriolis and the centripetal forces, resulting from the rotation of the earth, play a crucial role in such systems. For such applications it may be required to solve the system in complex three-dimensional geometries. In recent years, the Navier--Stokes equations in a rotating frame have been investigated in a number of papers using the classical inf-sup stable mixed methods, like Taylor-Hood pairs, to contribute to the analysis and the accurate and efficient numerical simulation. Numerical analysis reveals that these classical methods introduce a pressure-dependent contribution in the velocity error bounds that is proportional to some inverse power of the viscosity. Hence, these methods are optimally convergent but small velocity errors might not be achieved for complicated pressures and small viscosity coefficients. Several approaches have been proposed for improving the pressure-robustness of pairs of finite element spaces. In this contribution, a pressure-robust space discretization of the incompressible Navier--Stokes equations in a rotating frame of reference is considered. The discretization employs divergence-free, $H^1$-conforming mixed finite element methods like Scott--Vogelius pairs. However, this approach might come with a modification of the meshes, like the use of barycentric-refined grids in case of Scott--Vogelius pairs. However, this strategy requires the finite element code to have control on the mesh generator which is not realistic in many engineering applications and might also be in conflict with the solver for the linear system. An error estimate for the velocity is derived that tracks the dependency of the error bound on the coefficients of the problem, in particular on the angular velocity. Numerical examples illustrate the theoretical results. The idea of pressure-robust method could be cast on different types of flow problems which would be considered as future studies. As another future research direction, to avoid a modification of the mesh, one may use a very simple parameter-dependent modification of the Scott-Vogelius element, the pressure-wired Stokes element, such that the inf-sup constant is independent of nearly-singular vertices.

Keywords: navier-stokes equations in a rotating frame of refence, coriolis force, pressure-robust error estimate, scott-vogelius pairs of finite element spaces

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Authors: Alireza Vafaei Sadr, Vida Abedi, Jiang Li, Ramin Zand

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Missing data is a common challenge in medical research and can lead to biased or incomplete results. When the data bias leaks into models, it further exacerbates health disparities; biased algorithms can lead to misclassification and reduced resource allocation and monitoring as part of prevention strategies for certain minorities and vulnerable segments of patient populations, which in turn further reduce data footprint from the same population – thus, a vicious cycle. This study compares the performance of six imputation techniques grouped into Linear and Non-Linear models on two different realworld electronic health records (EHRs) datasets, representing 17864 patient records. The mean absolute percentage error (MAPE) and root mean squared error (RMSE) are used as performance metrics, and the results show that the Linear models outperformed the Non-Linear models in terms of both metrics. These results suggest that sometimes Linear models might be an optimal choice for imputation in laboratory variables in terms of imputation efficiency and uncertainty of predicted values.

Keywords: EHR, machine learning, imputation, laboratory variables, algorithmic bias

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Authors: Helmi Temimi

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In this paper, we study the super-convergence properties of the discontinuous Galerkin (DG) method applied to one-dimensional mth-order ordinary differential equations without introducing auxiliary variables. We found that nth−derivative of the DG solution exhibits an optimal O (hp+1−n) convergence rates in the L2-norm when p-degree piecewise polynomials with p≥1 are used. We further found that the odd-derivatives and the even derivatives are super convergent, respectively, at the upwind and downwind endpoints.

Keywords: discontinuous, galerkin, superconvergence, higherorder, error, estimates

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Authors: Young Hee Geum

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In this paper, we present the iterative method and determine the control parameters to converge cubically for solving nonlinear equations. In addition, we derive the asymptotic error constant.

Keywords: asymptotic error constant, iterative method, multiple root, root-finding, order of convergent

Procedia PDF Downloads 265

Authors: O. Benabdeljelil, A. Karioun, S. Amami, R. Rouger, M. Hamidine

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A model for preventing the risks related to climate conditions in the agricultural sector is presented. It will determine the yearly optimum premium to be paid by a producer in order to reach his required turnover. The model is based on both climatic stability and 'soft' responses of usually grown species to average climate variations at the same place and inside a safety ball which can be determined from past meteorological data. This allows the use of linear regression expression for dependence of production result in terms of driving meteorological parameters, the main ones of which are daily average sunlight, rainfall and temperature. By simple best parameter fit from the expert table drawn with professionals, optimal representation of yearly production is determined from records of previous years, and yearly payback is evaluated from minimum yearly produced turnover. The model also requires accurate pricing of commodity at N+1. Therefore, a pricing model is developed using 3 state variables, namely the spot price, the difference between the mean-term and the long-term forward price, and the long-term structure of the model. The use of historical data enables to calibrate the parameters of state variables, and allows the pricing of commodity. Application to beet sugar underlines pricer precision. Indeed, the percentage of accuracy between computed result and real world is 99,5%. Optimal premium is then deduced and gives the producer a useful bound for negotiating an offer by insurance companies to effectively protect its harvest. The application to beet production in French Oise department illustrates the reliability of present model with as low as 6% difference between predicted and real data. The model can be adapted to almost any agricultural field by changing state parameters and calibrating their associated coefficients.

Keywords: agriculture, production model, optimal price, meteorological factors, 3-factor model, parameter calibration, forward price

Procedia PDF Downloads 348

Authors: Mary Ann U. Baradi, Arnold R. Elepaño, Manuel Jose C. Regalado

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Aromatic rice has become popular and continues to command higher price than ordinary rice because of its distinctive scent that makes it special. Freshly harvested aromatic rice exhibits strong aromatic scent but decreases with time and conditions during storage. Of the many volatile compounds in aromatic rice, 2-acetyl-1-pyrroline (2AP) is a major compound that gives rice its popcorn-like aroma. The diffusion mechanism of 2AP in rice was investigated. Semi-empirical models explaining 2AP diffusion as affected by temperature and duration were developed. Storage time and temperature affected 2AP loss via diffusion. The amount of 2AP in rice decreased with time. Free 2AP, being volatile, is lost due to diffusion. Storage experiment indicated rapid 2AP loss during the first five weeks and subsequently leveled off afterwards; attaining level of starch bound 2AP. Decline of 2AP during storage followed exponential equation and exhibited four stages; i.e. the initial, second, third and final stage. Free 2AP is easily lost while bound 2AP is left, only to be released upon exposure to high temperature such as cooking. Both free and bound 2AP is found in endosperm while free 2AP is in the bran. Around 63–67% of total 2AP was lost in brown and milled rice of MS 6 paddy kept at ambient. Samples stored at higher temperature (27°C) recorded higher 2AP loss than those kept at lower temperature (15°C). The study should be able to guide processors in understanding and controlling parameters in storage to produce high quality rice.

Keywords: 2-acetyl-1-pyrroline, aromatic rice, diffusion mechanism, storage

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Authors: B. Siva Kumar Reddy, B. Lakshmi

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WiMAX has adopted an Adaptive Modulation and Coding (AMC) in OFDM to endure higher data rates and error free transmission. AMC schemes employ the Channel State Information (CSI) to efficiently utilize the channel and maximize the throughput and for better spectral efficiency. This CSI has given to the transmitter by the channel estimators. In this paper, LSE (Least Square Error) and MMSE (Minimum Mean square Error) estimators are suggested and BER (Bit Error Rate) performance has been analyzed. Channel equalization is also integrated with with AMC-OFDM system and presented with Constant Modulus Algorithm (CMA) and Least Mean Square (LMS) algorithms with convergence rates analysis. Simulation results proved that increment in modulation scheme size causes to improvement in throughput along with BER value. There is a trade-off among modulation size, throughput, BER value and spectral efficiency. Results also reported the requirement of channel estimation and equalization in high data rate systems.

Keywords: AMC, CSI, CMA, OFDM, OFDMA, WiMAX

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Authors: U. Sabura Banu, S. K. Lakshmanaprabu

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The improvement of meta-heuristic algorithm encourages control engineer to design an optimal controller for industrial process. Most real-world industrial processes are non-linear multivariable process with high interaction. Even in sub-process unit, thousands of loops are available mostly interacting in nature. Optimal controller design for such process are still challenging task. Closed loop controller design by multiloop PID involves a tedious procedure by performing interaction study and then PID auto-tuning the loop with higher interaction. Finally, detuning the controller to accommodate the effects of the other process variables. Fractional order PID controllers are replacing integer order PID controllers recently. Design of Multiloop Fractional Order (MFO) PID controller is still more complicated. Cuckoo algorithm, a swarm intelligence technique is used to optimally tune the MFO PID controller with easiness minimizing Integral Time Absolute Error. The closed loop performance is tested under servo, regulatory and servo-regulatory conditions.

Keywords: Cuckoo algorithm, mutliloop fractional order PID controller, two Interacting conical tank process

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Authors: Hyeonkyeong Yang, Minseok Son, Taekbeom Yoo, Woojin Park

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Human error is the most salient contributing factor to railway accidents. To reduce the frequency of human errors, many researchers and train designers have adopted ergonomic design principles for designing display-control layout in rail cab. There exist a number of approaches for designing the display control layout based on optimization methods. However, the ergonomically optimized layout design may not be the best design for train drivers, since the drivers have their own mental models based on their experiences. Consequently, the drivers may prefer the existing display-control layout design over the optimal design, and even show better driving performance using the existing design compared to that using the optimal design. Thus, in addition to ergonomic design principles, train drivers’ mental models also need to be considered for designing display-control layout in rail cab. This paper developed an ergonomic assessment system of display-control layout design, and an interactive layout design system that can generate design alternatives and calculate ergonomic assessment score in real-time. The design alternatives generated from the interactive layout design system may not include the optimal design from the ergonomics point of view. However, the system’s strength is that it considers train drivers’ mental models, which can help generate alternatives that are more friendly and easier to use for train drivers. Also, with the developed system, non-experts in ergonomics, such as train drivers, can refine the design alternatives and improve ergonomic assessment score in real-time.

Keywords: display-control layout design, interactive layout design system, mental model, train drivers

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Authors: Milca F. Coelho, K. Bousson, Kawser Ahmed

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To accurately track an aerospace vehicle in a time-critical situation and in a highly nonlinear environment, is one of the strongest interests within the aerospace community. The tracking is achieved by estimating accurately the state of a moving target, which is composed of a set of variables that can provide a complete status of the system at a given time. One of the main ingredients for a good estimation performance is the use of efficient estimation algorithms. A well-known framework is the Kalman filtering methods, designed for prediction and estimation problems. The success of the Kalman Filter (KF) in engineering applications is mostly due to the Extended Kalman Filter (EKF), which is based on local linearization. Besides its popularity, the EKF presents several limitations. To address these limitations and as a possible solution to tracking problems, this paper proposes the use of the Ensemble Kalman Filter (EnKF). Although the EnKF is being extensively used in the context of weather forecasting and it is being recognized for producing accurate and computationally effective estimation on systems with a very high dimension, it is almost unknown by the tracking community. The EnKF was initially proposed as an attempt to improve the error covariance calculation, which on the classic Kalman Filter is difficult to implement. Also, in the EnKF method the prediction and analysis error covariances have ensemble representations. These ensembles have sizes which limit the number of degrees of freedom, in a way that the filter error covariance calculations are a lot more practical for modest ensemble sizes. In this paper, a realistic simulation of a radar tracking was performed, where the EnKF was applied and compared with the Extended Kalman Filter. The results suggested that the EnKF is a promising tool for tracking applications, offering more advantages in terms of performance.

Keywords: Kalman filter, nonlinear state estimation, optimal tracking, stochastic environment

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Authors: Ho Yuan-Hong, Huang Chiung-Ju

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This study conducts simulation analyses to find the optimal debt ceiling of Taiwan, while factoring in welfare maximization under a dynamic stochastic general equilibrium framework. The simulation is based on Taiwan's 2001 to 2011 economic data and shows that welfare is maximized at a "debt"⁄"GDP" ratio of 0.2, increases in the "debt"⁄"GDP " ratio leads to increases in both tax and interest rates and decreases in the consumption ratio and working hours. The study results indicate that the optimal debt ceiling of Taiwan is 20% of GDP, where if the "debt"⁄"GDP" ratio is greater than 40%, the welfare will be negative and result in welfare loss.

Keywords: debt sustainability, optimal debt ceiling, dynamic stochastic general equilibrium, welfare maximization

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Authors: Toufic Sarieddine

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As the belt and road Initiative (henceforth, BRI) enters its 9th year, Iran and China are forging stronger ties on economic and military fronts, a development which has not only caused alarm in Washington but also risks staining China’s relationships with the oil-rich Gulf monarchies. World-systems theory has been used to examine the impact of the BRI on the current world order, with scholarship split on the capacity of China to emerge as a hegemon contending with the US or even usurping it. This paper argues the emergence of a new China-centered world-system comprised of states/areas and processes participating in the BRI and overlapping with the global world-system under (shaky) US hegemony. This world-system centers around China as core and hegemon via economic domination, capable new institutions (Shanghai Cooperation Council), legal modi operandi, the common goal of infrastructure development to rally support among developing states, and other indicators of hegemony outlined in world-systems theory. In this regard, while states like Pakistan could become peripheries to China in the BRI-bound world-system via large-scale projects such as the China-Pakistan Economic Corridor, Iran has greater capacities and influence in the Middle East, making it superior to a periphery. This paper thus argues that the increasing proximity between Iran and China sees the former becoming a semi-periphery with respect to China within the BRI-bound world-system, having economic dependence on its new core and hegemon while simultaneously wielding political and military influence on weaker states such as Iraq, Lebanon, Yemen, and Syria. The indicators for peripheralization as well as the characteristics of a semi-periphery outlined in world-systems theory are used to examine the current economic, political, and militaristic dimensions of Iran and China’s growing relationship, as well as the trajectory of these dimensions as part of the BRI-bound world-system.

Keywords: belt and road initiative, China, China-Middle East relations, Iran, world-systems analysis

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Authors: Lucian Mocan, Teodora Mocan, Matea Cristian, Cornel Iancu

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We present method of nanoparticle enhanced laser thermal ablation of Klebsiella pneumoniae infections, using gold nanoparticles combined with a specific growth factor and demonstrate its selective therapeutic efficacy. Ab (antibody solution) bound to GNPs (gold nanoparticles) was administered in vitro and determined the specific delivery of the nano-bioconjugate into the microorganism. The extent of necrosis was considerable following laser therapy, and at the same time, normal cells were not seriously affected. The selective photothermal ablation of the infected tissue was obtained after the selective accumulation of Ab bound to GNPs into bacteria following perfusion. These results may represent a major step in antibiotherapy treatment using nanolocalized thermal ablation by laser heating.

Keywords: gold nanoparticles, Klebsiella pneumoniae, nanoparticle functionalization, laser irradiation, antibody

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Authors: Mohamed Shawki Elamir, Heinrich Gotzig, Raoul Zoellner, Patrick Maeder

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In this work, a methodology is presented for identifying the optimal digitization parameters for the analog signal of ultrasonic sensors. These digitization parameters are the resolution of the analog to digital conversion and the sampling rate. This is accomplished through the derivation of characteristic curves based on Fano inequality and the calculation of the mutual information content over a given dataset. The mutual information is calculated between the examples in the dataset and the corresponding variation in the feature that needs to be estimated. The optimal parameters are identified in a manner that ensures optimal estimation performance while preventing inefficiency in using unnecessarily powerful analog to digital converters.

Keywords: analog to digital conversion, digitization, sampling rate, ultrasonic

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Authors: Yinggang Guo, Zongchun Li

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In order to decrease the accumulated survey error of tunnel installation control network of particle accelerator, a sectional control method is proposed. Firstly, the accumulation rule of positional error with the length of the control network is obtained by simulation calculation according to the shape of the tunnel installation-control-network. Then, the RMS of horizontal positional precision of tunnel backbone control network is taken as the threshold. When the accumulated error is bigger than the threshold, the tunnel installation control network should be divided into subsections reasonably. On each segment, the middle survey station is taken as the datum for independent adjustment calculation. Finally, by taking the backbone control points as faint datums, the weighted partial parameters adjustment is performed with the adjustment results of each segment and the coordinates of backbone control points. The subsections are jointed and unified into the global coordinate system in the adjustment process. An installation control network of the linac with a length of 1.6 km is simulated. The RMS of positional deviation of the proposed method is 2.583 mm, and the RMS of the difference of positional deviation between adjacent points reaches 0.035 mm. Experimental results show that the proposed sectional control method can not only effectively decrease the accumulated survey error but also guarantee the relative positional precision of the installation control network. So it can be applied in the data processing of tunnel installation control networks, especially for large particle accelerators.

Keywords: alignment, tunnel installation control network, accumulated survey error, sectional control method, datum

Procedia PDF Downloads 162

Authors: Sirus Mohammadi, Sara Ansari, Darush dehghan, Habib Hoshyari

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Batteries for storage of electricity from solar and wind generation farms are a key element in the success of sustainability. In recent years, due to large integration of Renewable Energy Sources (RESs) like wind turbine and photovoltaic unit into the Micro-Grid (MG), the necessity of Battery Energy Storage (BES) has increased dramatically. The BES has several benefits and advantages in the MG-based applications such as short term power supply, power quality improvement, facilitating integration of RES, ancillary service and arbitrage. This paper presents the cost-based formulation to determine the optimal size of the BES in the operation management of MG. Also, some restrictions, i.e. power capacity of Distributed Generators (DGs), power and energy capacity of BES, charge/discharge efficiency of BES, operating reserve and load demand satisfaction should be considered as well. In this paper, a methodology is proposed for the optimal allocation and economic analysis of ESS in MGs on the basis of net present value (NPV). As the optimal operation of an MG strongly depends on the arrangement and allocation of its ESS, economic operation strategies and optimal allocation methods of the ESS devices are required for the MG.

Keywords: microgrid, energy storage system, optimal sizing, net present value

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Authors: I. A. Farhat

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The dynamic economic dispatch (DED) problem is one of the complex, constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand. Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

Keywords: artificial immune system, dynamic economic dispatch, optimal economic operation, large-scale problem

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Authors: Lily Ingsrisawang, Tasanee Nacharoen

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Introduction: The problems of unbalanced data sets generally appear in real world applications. Due to unequal class distribution, many research papers found that the performance of existing classifier tends to be biased towards the majority class. The k -nearest neighbors’ nonparametric discriminant analysis is one method that was proposed for classifying unbalanced classes with good performance. Hence, the methods of discriminant analysis are of interest to us in investigating misclassification error rates for class-imbalanced data of three diabetes risk groups. Objective: The purpose of this study was to compare the classification performance between parametric discriminant analysis and nonparametric discriminant analysis in a three-class classification application of class-imbalanced data of diabetes risk groups. Methods: Data from a healthy project for 599 staffs in a government hospital in Bangkok were obtained for the classification problem. The staffs were diagnosed into one of three diabetes risk groups: non-risk (90%), risk (5%), and diabetic (5%). The original data along with the variables; diabetes risk group, age, gender, cholesterol, and BMI was analyzed and bootstrapped up to 50 and 100 samples, 599 observations per sample, for additional estimation of misclassification error rate. Each data set was explored for the departure of multivariate normality and the equality of covariance matrices of the three risk groups. Both the original data and the bootstrap samples show non-normality and unequal covariance matrices. The parametric linear discriminant function, quadratic discriminant function, and the nonparametric k-nearest neighbors’ discriminant function were performed over 50 and 100 bootstrap samples and applied to the original data. In finding the optimal classification rule, the choices of prior probabilities were set up for both equal proportions (0.33: 0.33: 0.33) and unequal proportions with three choices of (0.90:0.05:0.05), (0.80: 0.10: 0.10) or (0.70, 0.15, 0.15). Results: The results from 50 and 100 bootstrap samples indicated that the k-nearest neighbors approach when k = 3 or k = 4 and the prior probabilities of {non-risk:risk:diabetic} as {0.90:0.05:0.05} or {0.80:0.10:0.10} gave the smallest error rate of misclassification. Conclusion: The k-nearest neighbors approach would be suggested for classifying a three-class-imbalanced data of diabetes risk groups.

Keywords: error rate, bootstrap, diabetes risk groups, k-nearest neighbors

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Authors: Zainab Almukhtar, Adel Merabet

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In this paper, a method for maximum power point tracking of a photovoltaic energy conversion system is presented. This method is based on using the difference between the power from the solar panel and an estimated power value to control the DC-DC converter of the photovoltaic system. The difference is continuously compared with a preset error permitted value. If the power difference is more than the error, the estimated power is multiplied by a factor and the operation is repeated until the difference is less or equal to the threshold error. The difference in power will be used to trigger a DC-DC boost converter in order to raise the voltage to where the maximum power point is achieved. The proposed method was experimentally verified through a PV energy conversion system driven by the OPAL-RT real time controller. The method was tested on varying radiation conditions and load requirements, and the Photovoltaic Panel was operated at its maximum power in different conditions of irradiation.

Keywords: control system, error, solar panel, MPPT tracking

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Authors: Ranitha Guna Selvi D, Ramakrishnan R, Mohideen Abdul Kader

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Purpose: To study the role of Vision centers in managing preventable blindness through refractive error correction in Rural South India. Methods: A retrospective analysis of patients attending 15 Vision centers in Rural South India from a period of January 2021 to December 2021 was done. Medical records of 10,85,81 patients both new and reviewed, 79,562 newly registered patients and 29,019 review patient’s from15 Vision centers were included for data analysis. All the patients registered at the vision center underwent basic eye examination, including visual acuity, IOP measurement, Slit-lamp examination, retinoscopy, Fundus examination etc. Results: A total of 1,08,581 patients were included in the study. Of the total 1,08,581 patients, 79,562 were newly registered patients at Vision center and 29,019 were review patients. Males were 52,201(48.1%) and Females were 56,308(51.9) among them. The mean age of all examined patients was 41.03 ± 20.9 years (Standard deviation) and ranged from 01 – 113 years. Presenting mean visual acuity was 0.31 ± 0.5 in the right eye and 0.31 ± 0.4 in the left eye. Of the 1,08,581 patients 22,770 patients had refractive error in right eye and 22,721 patients had uncorrected refractive error in left eye. Glass prescription was given to 17,178 (15.8%) patients. 8,109 (7.5%) patients were referred to the base hospital for specialty clinic expert opinion or for cataract surgery. Conclusion: Vision center utilizing teleconsultation for comprehensive eye screening unit is a very effective tool in reducing the avoidable visual impairment caused due to uncorrected refractive error. Vision Centre model is believed to be efficient as it facilitates early detection and management of uncorrected refractive errors.

Keywords: refractive error, uncorrected refractive error, vision center, vision technician, teleconsultation

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Authors: Kathleen Joy Hingan, Jessiraye Luienne Catubigan, Carlo Mercado, Janisse RañEses

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In this research, the researchers wanted to explore how specialists and resident doctors in the fields of surgery, and obstetrics and gynecology handle their medical errors. They are interested in understanding the factors that contributed to the disclosure of medical error, the feelings after the occurrence of an error, and the way they coped with it given the power relations in place. The researchers conducted semi-structured interviews, transcribed the recordings, and analyzed the transcripts using thematic analysis. They found that doctors disclosed to their superiors and co-residents to cope with and to learn from the errors. In terms of disclosure to patients, the participants told them about the adverse event, but not about the error because of fear for themselves, their colleagues, their institution, and their patient. Doctors also performed compensatory actions to make up for the error and the nondisclosure of its occurrence. These actions functioned as a form of damage control too. Resident doctors and specialists receive different sanctions because of the power structures in the system.

Keywords: coping, disclosure, doctors, interviews, medical errors, thematic analysis

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Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

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The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f^-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: analytic functions, bi-univalent functions, Hohlov operator, subordination

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Authors: Yuekun Chen, Yousef Sardahi, Salam Hajjar, Christopher Greer

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This paper presents a multi-objective optimal design of a cascade control system for an underactuated mechanical system. Cascade control structures usually include two control algorithms (inner and outer). To design such a control system properly, the following conflicting objectives should be considered at the same time: 1) the inner closed-loop control must be faster than the outer one, 2) the inner loop should fast reject any disturbance and prevent it from propagating to the outer loop, 3) the controlled system should be insensitive to measurement noise, and 4) the controlled system should be driven by optimal energy. Such a control problem can be formulated as a multi-objective optimization problem such that the optimal trade-offs among these design goals are found. To authors best knowledge, such a problem has not been studied in multi-objective settings so far. In this work, an underactuated mechanical system consisting of a rotary servo motor and a ball and beam is used for the computer simulations, the setup parameters of the inner and outer control systems are tuned by NSGA-II (Non-dominated Sorting Genetic Algorithm), and the dominancy concept is used to find the optimal design points. The solution of this problem is not a single optimal cascade control, but rather a set of optimal cascade controllers (called Pareto set) which represent the optimal trade-offs among the selected design criteria. The function evaluation of the Pareto set is called the Pareto front. The solution set is introduced to the decision-maker who can choose any point to implement. The simulation results in terms of Pareto front and time responses to external signals show the competing nature among the design objectives. The presented study may become the basis for multi-objective optimal design of multi-loop control systems.

Keywords: cascade control, multi-Loop control systems, multiobjective optimization, optimal control

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Authors: M. Moradi Dalini, M. R. Talebi

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This research revolves around a technical method according to combines econometric and multiobjective programming to select and obtain optimal solutions to management problems. It is taken for a generation that; it is important to analyze which combination of values of the explanatory variables -in an econometric method- would point to the simultaneous achievement of the best values of the response variables. In this case, if a certain degree of conflict is viewed among the response variables, we suggest a multiobjective method in order to the results obtained from a regression analysis. In fact, with the use of a multiobjective method, we will have the best decision about the conflicting relationship between the response variables and the optimal solution. The combined multiobjective programming and econometrics benefit is an assessment of a balanced “optimal” situation among them because a find of information can hardly be extracted just by econometric techniques.

Keywords: econometrics, multiobjective optimization, management problem, optimization

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Authors: Longxiang Guo, Haoyan Hao, Xueli Sheng, Hanjun Yu, Jingwei Yin

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In order to prevent target splitting and ensure the accuracy of fusion, system error registration is an important step in multi-static sonar fusion detection system. To eliminate the inherent system errors including distance error and angle error of each sonar in detection, this paper uses offline estimation method for error registration. Suppose several sonars from different platforms work together to detect a target. The target position detected by each sonar is based on each sonar’s own reference coordinate system. Based on the two-dimensional stereo projection method, this paper uses real-time quality control (RTQC) method and least squares (LS) method to estimate sensor biases. The RTQC method takes the average value of each sonar’s data as the observation value and the LS method makes the least square processing of each sonar’s data to get the observation value. In the underwater acoustic environment, matlab simulation is carried out and the simulation results show that both algorithms can estimate the distance and angle error of sonar system. The performance of the two algorithms is also compared through the root mean square error and the influence of measurement noise on registration accuracy is explored by simulation. The system error convergence of RTQC method is rapid, but the distribution of targets has a serious impact on its performance. LS method can not be affected by target distribution, but the increase of random noise will slow down the convergence rate. LS method is an improvement of RTQC method, which is widely used in two-dimensional registration. The improved method can be used for underwater multi-target detection registration.

Keywords: data fusion, multi-static sonar detection, offline estimation, sensor registration problem

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Authors: Lina Wu, Jia Liu, Ye Li

Abstract:

The goal of this project is to investigate constant properties (called the Liouville-type Problem) for a p-stable map as a local or global minimum of a p-energy functional where the domain is a Euclidean space and the target space is a closed half-ellipsoid. The First and Second Variation Formulas for a p-energy functional has been applied in the Calculus Variation Method as computation techniques. Stokes’ Theorem, Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and the Bochner Formula as estimation techniques have been used to estimate the lower bound and the upper bound of the derived p-Harmonic Stability Inequality. One challenging point in this project is to construct a family of variation maps such that the images of variation maps must be guaranteed in a closed half-ellipsoid. The other challenging point is to find a contradiction between the lower bound and the upper bound in an analysis of p-Harmonic Stability Inequality when a p-energy minimizing map is not constant. Therefore, the possibility of a non-constant p-energy minimizing map has been ruled out and the constant property for a p-energy minimizing map has been obtained. Our research finding is to explore the constant property for a p-stable map from a Euclidean space into a closed half-ellipsoid in a certain range of p. The certain range of p is determined by the dimension values of a Euclidean space (the domain) and an ellipsoid (the target space). The certain range of p is also bounded by the curvature values on an ellipsoid (that is, the ratio of the longest axis to the shortest axis). Regarding Liouville-type results for a p-stable map, our research finding on an ellipsoid is a generalization of mathematicians’ results on a sphere. Our result is also an extension of mathematicians’ Liouville-type results from a special ellipsoid with only one parameter to any ellipsoid with (n+1) parameters in the general setting.

Keywords: Bochner formula, Calculus Stokes' Theorem, Cauchy-Schwarz Inequality, first and second variation formulas, Liouville-type problem, p-harmonic map

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Authors: Zubier Arfan, Paul Johnson

Abstract:

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

Procedia PDF Downloads 115

Authors: Filipe Cardoso de Oliveira, Lino Marcos da Silva, Ademar Nogueira do Nascimento, Cristiano Hora de Oliveira Fontes

Abstract:

This article presents a mathematical formulation for the production Break-Even Point problem in a non-homogeneous system. The optimization problem aims to obtain the composition of the best product mix in a non-homogeneous industrial plant, with the lowest cost until the breakeven point is reached. The problem constraints represent real limitations of a generic non-homogeneous industrial plant for n different products. The proposed model is able to solve the equilibrium point problem simultaneously for all products, unlike the existing approaches that propose a resolution in a sequential way, considering each product in isolation and providing a sub-optimal solution to the problem. The results indicate that the product mix found through the proposed model has economical advantages over the traditional approach used.

Keywords: branch and bound, break-even point, non-homogeneous production system, integer linear programming, management accounting

Procedia PDF Downloads 171

Authors: Said Algarni

Abstract:

The purpose of this study was to investigate selected numerical methods that demonstrate good performance in solving PDEs. We adapted alternative method that involve rational polynomials. Padé time stepping (PTS) method, which is highly stable for the purposes of the present application and is associated with lower computational costs, was applied. Furthermore, PTS was modified for our study which focused on diffusion equations. Numerical runs were conducted to obtain the optimal local error control threshold.

Keywords: Padé time stepping, finite difference, reaction diffusion equation, PDEs

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Authors: Adil Balla Elkrail

Abstract:

Visual MODFLOW computer codes were selected to simulate head distribution, calculate the groundwater budgets of the area, and evaluate the effect of external stresses on the groundwater head and to demonstrate how the groundwater model can be used as a comparative technique in order to optimize utilization of the groundwater resource. A conceptual model of the study area, aquifer parameters, boundary, and initial conditions were used to simulate the flow model. The trial-and-error technique was used to calibrate the model. The most important criteria used to check the calibrated model were Root Mean Square error (RMS), Mean Absolute error (AM), Normalized Root Mean Square error (NRMS) and mass balance. The maps of the simulated heads elaborated acceptable model calibration compared to observed heads map. A time length of eight years and the observed heads of the year 2004 were used for model prediction. The predictive simulation showed that the continuation of pumping will cause relatively high changes in head distribution and components of groundwater budget whereas, the low deficit computed (7122 m3/d) between inflows and outflows cannot create a significant drawdown of the potentiometric level. Hence, the area under consideration may represent a high permeability and productive zone and strongly recommended for further groundwater development.

Keywords: aquifers, model simulation, groundwater, calibrations, trail-and- error, prediction

Procedia PDF Downloads 212