scholarly journals A Neuro-Evolution Heuristic Using Active-Set Techniques to Solve a Novel Nonlinear Singular Prediction Differential Model

2022 ◽  
Vol 6 (1) ◽  
pp. 29
Author(s):  
Zulqurnain Sabir ◽  
Muhammad Asif Zahoor Raja ◽  
Thongchai Botmart ◽  
Wajaree Weera
Keyword(s):  
Numerical Solutions ◽  
Mean Squared Error ◽  
Merit Function ◽  
The Novel ◽  
Active Set ◽  
Shape Factors ◽  
Differential Model ◽  
Squared Error ◽  
Global And Local ◽  
Novel Design

In this study, a novel design of a second kind of nonlinear Lane–Emden prediction differential singular model (NLE-PDSM) is presented. The numerical solutions of this model were investigated via a neuro-evolution computing intelligent solver using artificial neural networks (ANNs) optimized by global and local search genetic algorithms (GAs) and the active-set method (ASM), i.e., ANN-GAASM. The novel NLE-PDSM was derived from the standard LE and the PDSM along with the details of singular points, prediction terms and shape factors. The modeling strength of ANN was implemented to create a merit function based on the second kind of NLE-PDSM using the mean squared error, and optimization was performed through the GAASM. The corroboration, validation and excellence of the ANN-GAASM for three distinct problems were established through relative studies from exact solutions on the basis of stability, convergence and robustness. Furthermore, explanations through statistical investigations confirmed the worth of the proposed scheme.

scholarly journals Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Juan L.G. Guirao ◽  
Zulqurnain Sabir ◽  
Tareq Saeed
Keyword(s):  
Numerical Solutions ◽  
Standard Form ◽  
Numerical Results ◽  
Third Order ◽  
Multiple Points ◽  
Shape Factors ◽  
Differential Model ◽  
Delay Differential ◽  
Global And Local ◽  
Novel Model

In this study, the design of a novel model based on nonlinear third-order Emden–Fowler delay differential (EF-DD) equations is presented along with two types using the sense of delay differential and standard form of the second-order EF equation. The singularity at ξ = 0 at single or multiple points of each type of the designed EF-DD model are discussed. The detail of shape factors and delayed points is provided for both types of the designed third-order EF-DD model. For the verification and validation of the model, two numerical examples are presented of each case and numerical results have been performed using the artificial neural network along with the hybrid of global and local capabilities. The comparison of the obtained numerical results with the exact solutions shows the perfection and correctness of the designed third-order EF-DD model.

scholarly journals Soft Computing Paradigms to Find the Numerical Solutions of a Nonlinear Influenza Disease Model

2021 ◽  
Vol 11 (18) ◽  
pp. 8549
Author(s):  
Zulqurnain Sabir ◽  
Ag Asri Ag Ibrahim ◽  
Muhammad Asif Zahoor Raja ◽  
Kashif Nisar ◽  
Muhammad Umar ◽  
...  
Keyword(s):  
Nonlinear System ◽  
Local Search ◽  
Objective Function ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Disease Model ◽  
Numerical Results ◽  
Active Set ◽  
System Equations ◽  
Global And Local

The aim of this work is to present the numerical results of the influenza disease nonlinear system using the feed forward artificial neural networks (ANNs) along with the optimization of the combination of global and local search schemes. The genetic algorithm (GA) and active-set method (ASM), i.e., GA-ASM, are implemented as global and local search schemes. The mathematical nonlinear influenza disease system is dependent of four classes, susceptible S(u), infected I(u), recovered R(u) and cross-immune individuals C(u). For the solutions of these classes based on influenza disease system, the design of an objective function is presented using these differential system equations and its corresponding initial conditions. The optimization of this objective function is using the hybrid computing combination of GA-ASM for solving all classes of the influenza disease nonlinear system. The obtained numerical results will be compared by the Adams numerical results to check the authenticity of the designed ANN-GA-ASM. In addition, the designed approach through statistical based operators shows the consistency and stability for solving the influenza disease nonlinear system.

scholarly journals Swarm Intelligence Procedures Using Meyer Wavelets as a Neural Network for the Novel Fractional Order Pantograph Singular System

2021 ◽  
Vol 5 (4) ◽  
pp. 277
Author(s):  
Zulqurnain Sabir ◽  
Muhammad Asif Zahoor Raja ◽  
Juan L. G. Guirao ◽  
Tareq Saeed
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Singular System ◽  
Standard Form ◽  
Merit Function ◽  
Stability And Convergence ◽  
Interior Point Algorithm ◽  
The Novel ◽  
Meyer Wavelets

The purpose of the current investigation is to find the numerical solutions of the novel fractional order pantograph singular system (FOPSS) using the applications of Meyer wavelets as a neural network. The FOPSS is presented using the standard form of the Lane–Emden equation and the detailed discussions of the singularity, shape factor terms along with the fractional order forms. The numerical discussions of the FOPSS are described based on the fractional Meyer wavelets (FMWs) as a neural network (NN) with the optimization procedures of global/local search procedures of particle swarm optimization (PSO) and interior-point algorithm (IPA), i.e., FMWs-NN-PSOIPA. The FMWs-NN strength is pragmatic and forms a merit function based on the differential system and the initial conditions of the FOPSS. The merit function is optimized, using the integrated capability of PSOIPA. The perfection, verification and substantiation of the FOPSS using the FMWs is pragmatic for three cases through relative investigations from the true results in terms of stability and convergence. Additionally, the statics’ descriptions further authorize the presentation of the FMWs-NN-PSOIPA in terms of reliability and accuracy.

A 3-R(SRS)RP Multi-Loop Mechanism for Space Manipulation: Design, Kinematics, Singularity, and Workspace

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Chuanyang Li ◽  
Hongwei Guo ◽  
Dewei Tang ◽  
Huiyin Yan ◽  
Rongqiang Liu ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
The Novel ◽  
Forward Displacement ◽  
Aerospace Applications ◽  
Wide Range ◽  
Variable Section ◽  
Varying Λ ◽  
Mapping Diagram ◽  
The Given ◽  
Novel Design

Abstract Space manipulation has great prospects in aerospace applications. In this work, a multiloop robot, namely 3-R(SRS)RP multiloop mechanism, is presented. Its design, kinematics, singularity, and workspace are studied. The novel design is mainly reflected in the robot’s structure, variable section, and novel compound hinge. Given these features, the forward-displacement undertaken with a closed-loop method leads to a complex mapping diagram. Only numerical solutions are obtained in this model due to the variable section parameter λ. This variable affects kinematic performances such as bending and folding properties. Moreover, the node differential kinematics and the Jacobian matrix are solved to analyze singular configurations of the mechanism. The workspace is then evaluated via a numerical method with varying λ. The bending and folding properties and the continuous workspace of the given robot vary while changing λ. Hence, the robot has great potentials of good performances in various applications. With this robot, a multimodule manipulator with a wide range of operations, increased mobility and rigidity, variable geometry, and adaptable shape based on mission requirements can be constructed.

scholarly journals Additive Dose Response Models: Explicit Formulations and the Loewe Additivity Consistency Condition

2017 ◽  
Author(s):  
Simone Lederer ◽  
Tjeerd M. H. Dijkstra ◽  
Tom Heskes
Keyword(s):  
Mean Squared Error ◽  
Reference Model ◽  
Consistency Condition ◽  
Data Sets ◽  
The Novel ◽  
Response Models ◽  
Reference Models ◽  
Squared Error ◽  
Common Principle ◽  
Loewe Additivity

AbstractHigh-throughput techniques allow for massive screening of drug combinations. To find combinations that exhibit an interaction effect, one filters for promising compound combinations by comparing to a response without interaction. A common principle for no interaction is Loewe Additivity which is based on the assumption that no compound interacts with itself and that doses of both compounds for a given effect are equivalent. For the model to be consistent, the doses of both compounds have to be proportional. We call this restriction the Loewe Additivity Consistency Condition (LACC). We derive explicit and implicit null reference models from the Loewe Additivity principle that are equivalent when the LACC holds. Of these two formulations, the implicit formulation is the known General Isobole Equation [1], whereas the explicit one is the novel contribution. The LACC is violated in a significant number of cases. In this scenario the models make different predictions. We analyze two data sets of drug screening that are non-interactive [2, 3] and show that the LACC is mostly violated and Loewe Additivity not defined. Further, we compare the measurements of the non-interactive cases of both data sets to the theoretical null reference models in terms of bias and mean squared error. We demonstrate that the explicit formulation of the null reference model leads to smaller mean squared errors than the implicit one and is much faster to compute.

scholarly journals Design of a Novel Second-Order Prediction Differential Model Solved by Using Adams and Explicit Runge–Kutta Numerical Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Zulqurnain Sabir ◽  
Juan L. G. Guirao ◽  
Tareq Saeed ◽  
Fevzi Erdoğan
Keyword(s):  
Numerical Methods ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Second Order ◽  
The Novel ◽  
Differential Model ◽  
Runge Kutta ◽  
Delay Differential ◽  
The Mind ◽  
Novel Model

In this study, a novel second-order prediction differential model is designed, and numerical solutions of this novel model are presented using the integrated strength of the Adams and explicit Runge–Kutta schemes. The idea of the present study comes to the mind to see the importance of delay differential equations. For verification of the novel designed model, four different examples of the designed model are numerically solved by applying the Adams and explicit Runge–Kutta schemes. These obtained numerical results have been compared with the exact solutions of each example that indicate the performance and exactness of the designed model. Moreover, the results of the designed model have been presented numerically and graphically.

scholarly journals A Novel Multi-Ionophore Approach for Potentiometric Analysis of Lanthanide Mixtures

Chemosensors ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 23
Author(s):  
Julia Ashina ◽  
Vasily Babain ◽  
Dmitry Kirsanov ◽  
Andrey Legin
Keyword(s):  
Spent Nuclear Fuel ◽  
Mean Squared Error ◽  
Sensor Arrays ◽  
Complex Mixture ◽  
Potentiometric Sensors ◽  
The Novel ◽  
Squared Error ◽  
Potentiometric Analysis ◽  
Array Performance ◽  
Extracting Agents

This work aims to discuss quantification of rare earth metals in a complex mixture using the novel multi-ionophore approach based on potentiometric sensor arrays. Three compounds previously tested as extracting agents in reprocessing of spent nuclear fuel were applied as ionophores in polyvinyl chloride (PVC)-plasticized membranes of potentiometric sensors. Seven types of sensors containing these ionophores were prepared and assembled into a sensor array. The multi-ionophore array performance was evaluated in the analysis of Ln3+ mixtures and compared to that of conventional monoionophore sensors. It was demonstrated that a multi-ionophore array can yield RMSEP (root mean-squared error of prediction) values not exceeding 0.15 logC for quantification of individual lanthanides in binary mixtures in a concentration range 5 to 3 pLn3+.

Use of reflectance spectroscopy to estimate the organic carbon and CaCO3 contents of soils

2012 ◽  
Vol 61 (2) ◽  
pp. 277-290 ◽  
Author(s):  
Ádám Csorba ◽  
Vince Láng ◽  
László Fenyvesi ◽  
Erika Michéli
Keyword(s):  
Organic Carbon ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Mean Squared Error ◽  
Reflectance Spectroscopy ◽  
Least Squares Regression ◽  
Root Mean Squared Error ◽  
Squared Error

Napjainkban egyre nagyobb igény mutatkozik olyan technológiák és módszerek kidolgozására és alkalmazására, melyek lehetővé teszik a gyors, költséghatékony és környezetbarát talajadat-felvételezést és kiértékelést. Ezeknek az igényeknek felel meg a reflektancia spektroszkópia, mely az elektromágneses spektrum látható (VIS) és közeli infravörös (NIR) tartományában (350–2500 nm) végzett reflektancia-mérésekre épül. Figyelembe véve, hogy a talajokról felvett reflektancia spektrum információban nagyon gazdag, és a vizsgált tartományban számos talajalkotó rendelkezik karakterisztikus spektrális „ujjlenyomattal”, egyetlen görbéből lehetővé válik nagyszámú, kulcsfontosságú talajparaméter egyidejű meghatározása. Dolgozatunkban, a reflektancia spektroszkópia alapjaira helyezett, a talajok ösz-szetételének meghatározását célzó módszertani fejlesztés első lépéseit mutatjuk be. Munkánk során talajok szervesszén- és CaCO3-tartalmának megbecslését lehetővé tévő többváltozós matematikai-statisztikai módszerekre (részleges legkisebb négyzetek módszere, partial least squares regression – PLSR) épülő prediktív modellek létrehozását és tesztelését végeztük el. A létrehozott modellek tesztelése során megállapítottuk, hogy az eljárás mindkét talajparaméter esetében magas R2értéket [R2(szerves szén) = 0,815; R2(CaCO3) = 0,907] adott. A becslés pontosságát jelző közepes négyzetes eltérés (root mean squared error – RMSE) érték mindkét paraméter esetében közepesnek mondható [RMSE (szerves szén) = 0,467; RMSE (CaCO3) = 3,508], mely a reflektancia mérési előírások standardizálásával jelentősen javítható. Vizsgálataink alapján arra a következtetésre jutottunk, hogy a reflektancia spektroszkópia és a többváltozós kemometriai eljárások együttes alkalmazásával, gyors és költséghatékony adatfelvételezési és -értékelési módszerhez juthatunk.

Using Approximation Non-Bayesian Computation with Fuzzy Data to Estimation Inverse Weibull Parameters and Reliability Function

2018 ◽  
pp. 397
Author(s):  
Nadia Hashim Al-Noor ◽  
Shurooq A.K. Al-Sultany
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Mean Squared Error ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Fuzzy Data ◽  
Monte Carlo Simulation Study ◽  
Weibull Parameters ◽  
Squared Error ◽  
Newton Raphson

        In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function in terms of their mean squared error values and integrated mean squared error values respectively.

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