Error Analysis Technique Research Articles

A computational approach for solving second-order nonlinear ordinary differential equations by means of Laguerre series

In this work, a novel efficient numeric procedure for obtaining the approximate solution of a class of second-order nonlinear ordinary differential equations is presented which play a significant part in science and engineering branches. The technique is based on matrix equations and collocation points with truncated Laguerre series. The acquired approximate solutions subject to initial conditions are obtained in terms of Laguerre polynomials. Also, some examples together with error analysis techniques are acquired to demonstrate the efficacy of the present method, and the comparisons are made with current studies.

Adsorptive eradication of tartrazine from aqueous solutions onto doped polyaniline

A potential polymeric adsorbent, doped polyaniline (PANI) has been investigated for the eradication of the hazardous dye tartrazine from textile effluent. During the adsorption process, the influence of the acidic character of the adsorbate, pH, dose of the adsorbent, dye concentration and time of contact between the adsorbent and adsorbate were evaluated. The outcomes attained from batch experiments were applied to the Langmuir and the Freundlich isothermal models. Different error analysis techniques, such as mean square error, root mean square error, the Chi-square test (?2), sum of absolute errors and sum of squared errors, were determined for the doped polyaniline?tartrazine system. The Langmuir isotherm was established as the best-fit isothermal model, with minimum errors and high regression values. About 90?97 % removal was achieved in the first 70 min. A positive enthalpy value implied the adsorption process was endothermic. The energy of activation for the dye adsorbent system was found to be 28.9 kJ mol-1, which is in line with physisorption.

Influence of geometric parameters on the bump foil bearing performance

High-speed rotating system development has drawn considerable attention of the researchers, in the recent past. Foil bearings are one of the major contenders for such applications, particularly for high speed and low load rotating systems. In foil bearings, process fluid or air is used as the working medium and no additional lubricant is required. It is known from the published literature that the load capacity of foil bearings depend on the operating speed, viscosity of the medium, clearance, and stiffness of the foil apart from the geometric dimensions of the bearing. In case of foil bearing with given dimensions, clearance governs the magnitude of pressure developed, whereas stiffness dictates the change in radial clearance under the generated pressure. This article deals with the effect of stiffness, clearance, and its interaction on the bump foil bearings load-carrying capacity. For this study, four sets of foil bearings of the same geometry with two levels of stiffness and clearance values are fabricated. Experiments are carried out following two factor-two level factorial design approach under constant load and in each case, the lift-off speed is measured. The experimental output is analyzed using statistical techniques to evaluate the influence of parameters under consideration. The results indicate that clearance has the maximum influence on the lift-off speed/ load-carrying capacity, followed by interaction effect and stiffness. A regression model is developed based on the experimental values and model is validated using error analysis technique.

An integrated numerical method with error analysis for solving fractional differential equations of quintic nonlinear type arising in applied sciences

In this study, fractional differential equations having quintic nonlinearity are considered by proposing an accurate numerical method based on the matching polynomial and matrix‐collocation system. This method provides an integration between matrix and fractional derivative, which makes it fast and efficient. A hybrid computer program is designed by making use of the fast algorithmic structure of the method. An error analysis technique consisting of the fractional‐based residual function is constructed to scrutinize the precision of the method. Some error tests are also performed. Figures and tables present the consistency of the approximate solutions of highly stiff model problems. All results point out that the method is effective, simple, and eligible.

A priori $$\varvec{L^{\infty }(L^2)}$$ error estimates for finite element approximations to parabolic integro-differential equations with discontinuous coefficients

Finite element treatment for parabolic integro-differential equations with discontinuous coefficients are presented in this work. Due to low global regularity of the solutions, the error analysis technique of the standard finite element method is difficult to adopt for interface problems. In this paper, convergence of continuous time Galerkin method for the spatially discrete scheme and backward difference scheme in time direction are discussed in $$L^{\infty }(L^2)$$ norm for fitted finite element method with straight interface triangles. More precisely, optimal error estimates are derived in $$L^{\infty }(L^2)$$ norm when initial data $$u_0\in H^3\cap H_0^1(\Omega )$$ . The interface is assumed to be smooth for our purpose.

Measurements and modelling of CH4 and CO2 adsorption behaviors on shales: Implication for CO2 enhanced shale gas recovery

A thorough study of the adsorption behavior of shales to methane (CH4) and carbon dioxide (CO2) is critical for carbon dioxide sequestration in shale gas reservoirs and enhanced shale gas recovery. This paper discusses the results of an adsorption study of CH4 and CO2, in single gas environment, on a set of shale samples taken from the Sichuan and Ordos Basins. The results indicated that shale exhibit higher affinity to CO2 as compared to CH4 under similar pressure and temperature conditions, and the preferential adsorption ratio of CO2 over CH4 varies between 1.66 and 8.32. Furthermore, the experimental data were modeled using Langmuir, Dubibin-Astakhov (D-A), Dubinin-Redushckevich (D-R) and Ono-Kondo models. The accuracy of the models in quantifying CH4 and CO2 adsorption on shale was compared using an error analysis technique. For CH4, both of Langmuir and D-A models performed satisfactorily with comparable accuracy. For subcritical CO2, the performance of the D-A model is the best. However, for supercritical CO2, Ono-Kondo model fitted the experimental data the best, which is the proposed model to use. The results of this study can provide the basis for the estimation of the CO2 sequestration capacity in shale formations.

A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types

In this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor the usefulness of the method. All results are scrutinized in tables and figures. Finally, an illustrative algorithm is presented.

Oil Demand Forecasting in Malaysia in Transportation Sector Using Artificial Neural Network

Energy industry in Malaysia is one of critical sector that plays a major role in contributing the nation economic and industrial growth. A forecasting model is required to be developed to provide the oil demand forecast in transportation sector. This research analyses different forecasting models including Artificial Neural Network (ANN) model to predict the future oil demand in transportation sector in Malaysia. In order to select the best forecasting model, the model validation is done using the error analysis techniques. Based on the model validation result, it is found that the Artificial Neural Network (Multivariate) model gives the least error in all the error analysis techniques. The model forecast that the oil demand in transportation sector in Malaysia for the year 2020, 2025 and 2030 would be 559.44, 581.779 and 609.941 kg of oil equivalent respectively.

An Analytical Approach for Error PMF Characterization in Approximate Circuits

Approximate computing has emerged as a circuit design technique that can reduce system power without significantly sacrificing the output quality in error-resilient applications. However, there exists only a few approaches for systematically and efficiently determining the error introduced by approximate hardware units. This paper focuses on the development of error analysis techniques for approximate circuits consisting of adders and multipliers, which are the key hardware components used in error-resilient applications. A novel algorithm has been presented, using the Fourier and the Mellin transforms, that efficiently determines the probability distribution of the error introduced by approximation in a circuit, abstracted as a directed acyclic graph. The algorithm is generalized for signed operations through two’s complement representation, and its accuracy is demonstrated to be within 1% of Monte Carlo simulations, while being over an order of magnitude faster.

A NEW NUMERICAL METHOD FOR SOLVING FUNCTIONAL DELAY INTEGRAL EQUATIONS WITH VARIABLE BOUNDS BY USING GENERALIZED MOTT POLYNOMIALS

In this study, the functional delay integral equations with variable bounds are considered. Their approximate solutions are obtained by using a new method based on matrix, collocation points and the generalized Mott polynomials with the parameter-$\beta$. An error analysis technique consisting of the residual function is performed. The numerical examples are illustrated for the practicability and usability of the method. The behavior of the solutions is monitored in terms of the parameter-$\beta$. The accuracy of the method is scrutinized for different values of N. In addition, the numerical results are discussed in figures and tables.

An Analysis on Undergraduate Students’ Abstracts at English Education Department in Manado State University

The aim of this research was to find out and identify grammatical errors contained in abstract of undergraduate theses written by students at English Education Department in Manado State University. This research used descriptive method. In the data gathering, this study applied purposive sampling technique. The subject of this research was 50 abstracts of undergraduate theses published only in 2018 and then analyzed by using error analysis technique. Based on the findings, the most frequent error made by the students was omission with 19 errors (37.25%), addition with 8 errors (15.68%), archiform with 6 errors (11.76%), misformation with 11 errors (21.56%), and the least was misordering with 2 errors (3.92 %). This shows that there is still need for improvement in grammar teaching and learning for academic writing should be free from grammatical mistakes. From 50 abstracts documented by the researcher, there are only 21 abstract which are grammatically correct, and 29 abstracts contain 51 errors. Since abstract is the published piece for research report by graduated students, there should be more concern in abstract writing, particularly its accuracy in grammar.Keywords: Grammatical error, abstract, undergraduate thesis, English Education Department

Evolving robust intelligent model based on group method of data handling technique optimized by genetic algorithm to predict asphaltene precipitation

Precipitation of asphaltene during primary production of hydrocarbon reservoirs leads to formation damage and well bore plugging. Therefore, proposing an accurate model to estimate asphaltene precipitation under various operating and thermodynamic conditions are crucial. In this study, a new mathematical model based on the integrating group method of data handling (GMDH) with genetic algorithm has been developed to predict asphaltene precipitation as a function of reservoir pressure and temperature, crude oil API, bubble point pressure, Saturated-Aromatic-Resin-Asphaltene (SARA) fractions and mole percent of non-hydrocarbon gases. Genetic algorithm technique has been applied to optimize the most appropriate network structure of GMDH model. In order to accomplish modeling, asphaltene precipitation of different crude oils from a number of Iranian reservoirs at wide ranges of operating conditions have been measured experimentally and applied for network construction. The accuracy of developed model has been evaluated by both statistical and graphical error analysis techniques. The average absolute relative deviation of the proposed model is 3.65%, which indicates model predictions are in excellent agreement with experimental data. Also, the comparison of developed GMDH model with scaling equation and least squares support vector machine (LSSVM) reveals the superiority of the proposed GMDH structure in prediction of asphaltene precipitation over scaling equation and LSSVM technique. In addition, the Leverage approach has been applied to detect suspected data. The results show that all experimental data are reliable and located within the applicable domain of developed model. Finally, a comprehensive sensitivity analysis based on the relevancy factor has been carried out which shows that percentages of resin and saturated components have the largest direct and inverse impacts on asphaltene precipitation, respectively.

Attitude of Nonlanguage Program Students Toward the Indonesian Language at the Universitas Mulawarman

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A numerical technique for solving functional integro-differential equations having variable bounds

In this paper, a collocation method based on Taylor polynomials is presented to solve the functional delay integro-differential equations with variable bounds. Using this method, we transform the functional equations to a system of linear algebraic equations. Thus, the unknown coefficients of the approximate solution are determined by solving this system. An error analysis technique based on residual function is developed to improve the numerical solution. Some numerical examples are given to illustrate the accuracy and applicability of the method. Finally, the data are examined according to the residual error estimation. All numerical computations have been performed on the computer programs.

A new organization-oriented technique of human error analysis in digital NPPs: Model and classification framework

In nuclear power plants (NPPs), man-machine interfaces (MMIs) are being transformed from conventional panels to computer workstations. Therefore, operators’ behavior and performance shaping factors (PSFs) in modern main control rooms (MCRs) differs from what they do in a conventional one. New human error, error mechanism and PSFs etc. are introduced into digital control systems (DCS). The conventional human error analysis (HEA) methods cannot meet new requirements. So it is important to establish a new technique of HEA for investigating human failure events in digital NPPs. In order to investigate and analyze human errors and to trace organizational root causes in digital NPPs, an Organization-oriented Technique of Human Error Analysis (OTHEA) was established. At this first paper, an organization-oriented conceptual model of HEA was established. Furthermore, the classification framework of HEA was developed based on the established conceptual model of HEA, including classification of human error, PSFs, psychological error mechanisms (PEMs), error recovery failures (ERFs) and safety barriers. It provides a theoretical guidance and practical support for the investigation of human failure events in digital NPPs.

Morbidity and Mortality Conferences: A Mini Review and Illustrated Application in Veterinary Medicine.

This mini review presents current knowledge on the role of morbidity and mortality conferences (M&MCs) as a powerful educational tool and driver to improve patient care. Although M&MCs have existed since the early twentieth century, formal evaluation of their impact on education and patient care is relatively recent. Over time, M&MCs have evolved from single discipline discussions with a tendency to focus on individual errors and assign blame, to multidisciplinary, standardized presentations incorporating error analysis techniques, and educational theory. Current evidence shows that M&MCs can provide a valuable educational experience and have the potential to generate measurable improvements in patient care.

Assessing Constitutive Models for Prediction of High-Temperature Flow Behavior with a Perspective of Alloy Development

The utility of different constitutive models describing high-temperature flow behavior has been evaluated from the perspective of alloy development. Strain compensated Arrhenius model, modified Johnson–Cook (MJC) model, model D8A and artificial neural network (ANN) have been used to describe flow behavior of different model alloys. These alloys are four grades of SS 316LN with different nitrogen contents ranging from 0.07 to 0.22%. Grades with 0.07%N and 0.22%N have been used to determine suitable material constants of the constitutive equations and also to train the ANN model. While the ANN model has been developed with chemical composition as a direct input, the MJC and D8A models have been amended to incorporate the effect of nitrogen content on flow behavior. The prediction capabilities of all models have been validated using the experimental data obtained from grades containing 0.11%N and 0.14%N. The comparative analysis demonstrates that ‘N-amended D8A’ and ‘N-amended MJC’ are preferable to the ANN model for predicting flow behavior of different grades of 316LN. The work provides detailed insights into the usual statistical error analysis technique and frames five additional criteria which must be considered when a model is analyzed from the perspective of alloy development.

A new error analysis technique for cooperative 5G systems

Deployment of cooperative techniques on 5G cellular networks has been a subject of recent interest to researchers. A cooperative diversity relay system has a root terminal, an intermediate terminal and an end terminal is presented. The intermediate terminal detects the root terminal’s information through the decode and forward protocol and forwards it to the end terminal. The authors have proposed a new switched diversity scheme for the above system and have done a mathematical investigation of its performance. In the flat Rayleigh fading environment with phase shift keying modulation, the symbol error probability has been derived for a cooperative diversity system. The proposed scheme has been compared against other competing schemes seen in literature. The numerical results have revealed a better performance of the proposed system than the existing system.

Laguerre Series Solutions of the Delayed Single Degree-of-Freedom Oscillator Excited by an External Excitation and Controlled by a Control Force

With increasing technologies, applications of delayed models are more frequently encountered in biology, physics and various fields of engineering. The single degree-of-freedom oscillator, on the other hand, is one of the fundamental systems in many physics and engineering problems; thus, solving the equation of this problem would serve for many other sophisticated problems. In this study, a novel and simple numerical method for the solution of this system is introduced in the matrix form based on Laguerre polynomials. The method is exemplified through a numerical application and the results obtained are compared with those of another method. In addition, an error analysis technique based on residual function is developed and applied to this problem to demonstrate the validity and applicability of the method. The convenience of the method is that it is quite simple to employ by using computer programs.

Computing Effective Diffusivity of Chaotic and Stochastic Flows Using Structure-Preserving Schemes

In this paper, we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition, we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual diffusion refers to the nonzero effective (homogenized) diffusion in the limit of zero molecular diffusion as a result of chaotic mixing of the streamlines. In this limit, traditional numerical methods typically fail since the solutions of the advection-diffusion equations develop sharp gradients. Instead of solving the Fokker--Planck equation in the Eulerian formulation, we compute the motion of particles in the Lagrangian formulation, which is modeled by stochastic differential equations (SDEs). We propose an effective numerical integrator based on a splitting method to solve the corresponding SDEs in which the deterministic subproblem is symplectic preserving while the random subproblem can be viewed as a perturbation. We provide rigorous error analysis for the new numerical integrator using the backward error analysis technique and show that our method outperforms standard Euler-based integrators. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several typical chaotic and stochastic flow problems of physical interest. The existence of residual diffusivity for these flow problems is also investigated.