Identifying an unknown potential term in the fourth-order Boussinesq–Love equation from mass measurement

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mousa Huntul ◽  
Mohammad Tamsir
Keyword(s):  
Inverse Problem ◽  
Fourth Order ◽  
Input Data ◽  
Mass Measurement ◽  
Potential Coefficient ◽  
Content Type ◽  
Von Neumann ◽  
Potential Term ◽  
Noisy Input ◽  
Von Neumann Stability Analysis

PurposeThe inverse problem of identifying the time-dependent potential coefficient along with the temperature in the fourth-order Boussinesq–Love equation (BLE) with initial and boundary conditions supplemented by mass measurement is, for the first time, numerically investigated. From the literature, the authors already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data.Design/methodology/approachFor the numerical discretization, the authors apply the Crank–Nicolson finite difference method along with the Tikhonov regularization for finding a stable and accurate approximate solution. The resulting nonlinear minimization problem is solved using the MATLAB routine lsqnonlin. Both exact and numerically simulated noisy input data are inverted.FindingsThe present computational results demonstrate that obtained solutions are stable and accurate.Originality/valueThe inverse problem presented in this paper was already showed to be locally uniquely solvable, but no numerical identification has been studied yet. Therefore, the main aim of the present work is to undertake the numerical realization. The von Neumann stability analysis is also discussed.

scholarly journals Determination of the time-dependent convection coefficient in two-dimensional free boundary problems

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mousa Huntul ◽  
Daniel Lesnic
Keyword(s):  
Inverse Problem ◽  
Free Boundary ◽  
Numerical Solution ◽  
Input Data ◽  
Free Boundary Problems ◽  
Time Dependent ◽  
Two Dimensional ◽  
Convection Coefficient ◽  
Content Type ◽  
Noisy Input

Purpose The purpose of the study is to solve numerically the inverse problem of determining the time-dependent convection coefficient and the free boundary, along with the temperature in the two-dimensional convection-diffusion equation with initial and boundary conditions supplemented by non-local integral observations. From the literature, there is already known that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. Design/methodology For the numerical discretization, this paper applies the alternating direction explicit finite-difference method along with the Tikhonov regularization to find a stable and accurate numerical solution. The resulting nonlinear minimization problem is solved computationally using the MATLAB routine lsqnonlin. Both exact and numerically simulated noisy input data are inverted. Findings The numerical results demonstrate that accurate and stable solutions are obtained. Originality/value The inverse problem presented in this paper was already showed to be locally uniquely solvable, but no numerical solution has been realized so far; hence, the main originality of this work is to attempt this task.

An inverse problem of determining the time-dependent potential in a higher-order Boussinesq-Love equation from boundary data

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mousa Huntul ◽  
Mohammad Tamsir ◽  
Abdullah Ahmadini
Keyword(s):  
Inverse Problem ◽  
Boundary Data ◽  
Numerical Solutions ◽  
Physical Property ◽  
Neumann Boundary ◽  
Higher Order ◽  
Time Dependent ◽  
Potential Coefficient ◽  
Content Type ◽  
Dependent Potential

PurposeThe paper aims to numerically solve the inverse problem of determining the time-dependent potential coefficient along with the temperature in a higher-order Boussinesq-Love equation (BLE) with initial and Neumann boundary conditions supplemented by boundary data, for the first time.Design/methodology/approachFrom the literature, the authors already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. For the numerical realization, the authors apply the generalized finite difference method (GFDM) for solving the BLE along with the Tikhonov regularization to find stable and accurate numerical solutions. The regularized nonlinear minimization is performed using the MATLAB subroutine lsqnonlin. The stability analysis of solution of the BLE is proved using the von Neumann method.FindingsThe present numerical results demonstrate that obtained solutions are stable and accurate.Practical implicationsSince noisy data are inverted, the study models real situations in which practical measurements are inherently contaminated with noise.Originality/valueThe knowledge of this physical property coefficient is very important in various areas of human activity such as seismology, mineral exploration, biology, medicine, quality control of industrial products, etc. The originality lies in the insight gained by performing the numerical simulations of inversion to find the potential co-efficient on time in the BLE from noisy measurement.

scholarly journals An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. J. Huntul ◽  
Muhammad Abbas ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Input Data ◽  
Time Dependent ◽  
One Dimensional ◽  
Noisy Input ◽  
Nonlinear Minimization ◽  
Ill Posed ◽  
Dependent Potential ◽  
The Stability ◽  
First Time

AbstractIn this paper, for the first time the inverse problem of reconstructing the time-dependent potential (TDP) and displacement distribution in the hyperbolic problem with periodic boundary conditions (BCs) and nonlocal initial supplemented by over-determination measurement is numerically investigated. Though the inverse problem under consideration is ill-posed by being unstable to noise in the input data, it has a unique solution. The Crank–Nicolson-finite difference method (CN-FDM) along with the Tikhonov regularization (TR) is applied for calculating an accurate and stable numerical solution. The programming language MATLAB built-in lsqnonlin is used to solve the obtained nonlinear minimization problem. The simulated noisy input data can be inverted by both analytical and numerically simulated. The obtained results show that they are accurate and stable. The stability analysis is performed by using Fourier series.

An efficient application of PML in fourth-order precise integration time domain method for the numerical solution of Maxwell's equations

2013 ◽  
Vol 33 (1/2) ◽  
pp. 116-125
Author(s):  
Zhongming Bai ◽  
Xikui Ma ◽  
Xu Zhuansun ◽  
Qi Liu
Keyword(s):  
Finite Difference ◽  
Numerical Solution ◽  
Fourth Order ◽  
Time Domain ◽  
Fdtd Method ◽  
Time Domain Method ◽  
Integration Time ◽  
Precise Integration ◽  
Content Type ◽  
Domain Method

Purpose – The purpose of the paper is to introduce a perfectly matched layer (PML) absorber, based on Berenger's split field PML, to the recently proposed low-dispersion precise integration time domain method using a fourth-order accurate finite difference scheme (PITD(4)). Design/methodology/approach – The validity and effectiveness of the PITD(4) method with the inclusion of the PML is investigated through a two-dimensional (2-D) point source radiating example. Findings – Numerical results indicate that the larger time steps remain unchanged in the procedure of the PITD(4) method with the PML, and meanwhile, the PITD(4) method employing the PML is of the same absorbability as that of the finite-difference time-domain (FDTD) method with the PML. In addition, it is also demonstrated that the later time reflection error of the PITD(4) method employing the PML is much lower than that of the FDTD method with the PML. Originality/value – An efficient application of PML in fourth-order precise integration time domain method for the numerical solution of Maxwell's equations.

A cost evaluation model for IoT-enabled prefabricated construction supply chain management

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wennan Zhang ◽  
Kai Kang ◽  
Ray Y. Zhong
Keyword(s):  
Hong Kong ◽  
Supply Chain ◽  
Input Data ◽  
Evaluation Model ◽  
Construction Cost ◽  
Influential Factors ◽  
System Boundary ◽  
Supply Chain System ◽  
Content Type ◽  
The Relationship

PurposeThis paper proposes an evaluation model for prefabricated construction to guide a supply chain with controllable costs. Prefabricated construction is prevalent due to area limitations. Nevertheless, the development is limited by budget control and identifying the factors affecting cost. The degree of close collaboration in the supply chain is closely interconnected with cost performance that includes direct and indirect factors. This paper not only quantizes these factors but also distinguishes the degree of influence of various factors.Design/methodology/approachSystem dynamics is applied to simulate and analyze the construction cost factors through Vensim software. It can also clarify the relationship between cost and other influencing factors. The input data are collected from an Internet of Things (IoT)-enabled system under a Building Information Modeling (BIM) system and Hong Kong government reports.FindingsSimulation results indicate that prefabricated construction cost is mainly influenced by government promotion degree (GPD), working pressure from on-site construction (WPOSC), prefab quality (PQ), load-bearing capacity per vehicle (LBPV) and mold quality (MQ). However, it is more sensitive toward GPD, which indicates that the government should take measures to promote this construction technology. On-site worker management is also essential for the assembly process and indirectly influences the construction cost.Research limitations/implicationsThis paper quantifies indirect influential factors to clarify the specific features for prefabricated construction. The investigated factors are limited.Practical implicationsThe contractor can identify all factors and classify the levels of influence to make decisions under the supply chain system boundary.Social implicationsThe input data are collected from an IoT-enabled system under a BIM system and Hong Kong government reports. Thus, the relationship between construction cost influential factors can be investigated.Originality/valueThis paper quantifies indirect influencing factors and clarifies the specific features in prefabricated construction. The contractor could identify these factors to make decisions and classify the levels of influence under the supply chain system boundary.

Pitting corrosion prediction from cathodic data: application of machine learning

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohamed Nadir Boucherit ◽  
Fahd Arbaoui
Keyword(s):  
Machine Learning ◽  
Physicochemical Properties ◽  
Input Data ◽  
Surface Condition ◽  
Recurrent Network ◽  
Localized Corrosion ◽  
Potential Region ◽  
Pitting Potential ◽  
Content Type ◽  
Nuclear Installation

Purpose To constitute input data, the authors carried out electrochemical experiments. The authors performed voltammetric scans in a very cathodic potential region. The authors constituted an experimental table where for each experiment we note the current values recorded at a low polarization range and the pitting potential observed in the anodic region. This study aims to concern carbon steel used in a nuclear installation. The properties of the chemical solutions are close to that of the cooling fluid used in the circuit. Design/methodology/approach In a previous study, this paper demonstrated the effectiveness of machine learning in predicting the localized corrosion resistance of a material by considering as input data the physicochemical properties of its environment (Boucherit et al., 2019). With the present study, the authors improve the results by considering as input data, cathodic currents. The reason of such an approach is to have input data that integrate both the surface state of the material and the physicochemical properties of its environment. Findings The experimental table was submitted to two neural networks, namely, a recurrent network and a convolution network. The convolution network gives better pitting potential predictions. Results also prove that the prediction by observing cathodic currents is better than that obtained by considering the physicochemical properties of the solution. Originality/value The originality of the study lies in the use of cathodic currents as input data. These data contain implicit information on both the chemical environment of the material and its surface condition. This approach appears to be more efficient than considering the chemical composition of the solution as input data. The objective of this study remains, at the same time, to seek the optimal neuronal architectures and the best input data.

scholarly journals Neural Networks Art: Solving Problems with Multiple Solutions and New Teaching Algorithm

2014 ◽  
Vol 8 (1) ◽  
pp. 15-21
Author(s):  
Dmitrienko V. D ◽  
Yu. Zakovorotnyi A ◽  
Yu. Leonov S ◽  
Khavina I. P
Keyword(s):  
Neural Networks ◽  
Multiple Solutions ◽  
Input Data ◽  
Learning Algorithms ◽  
Adaptive Resonance Theory ◽  
Classification Methods ◽  
Resonance Theory ◽  
Adaptive Resonance ◽  
Noisy Input ◽  
New Algorithms

A new discrete neural networks adaptive resonance theory (ART), which allows solving problems with multiple solutions, is developed. New algorithms neural networks teaching ART to prevent degradation and reproduction classes at training noisy input data is developed. Proposed learning algorithms discrete ART networks, allowing obtaining different classification methods of input.

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