This paper presents a study of the performance of the Tau method using Chebyshev basis functions for solving fourth-order differential equation with boundary conditions. Existence and uniqueness of the solution of this equation are investigated transforming it into the Volterra–Fredholm integral equation. We use the operational Tau matrix representation with Chebyshev basis functions for constructing

We propose a regularization method based on the iterative conjugate gradient method for the solution of a Cauchy problem for the wave equation in one dimension. This linear but ill-posed Cauchy problem consists of finding the displacement and flux on a hostile and inaccessible part of the medium boundary from Cauchy data measurements of the same quantities on the remaining friendly and accessible part

Principal component analysis (PCA) methods have been widely applied to damage identification in the long-term structural health monitoring (SHM) of infrastructure. Usually, the first few eigenvector components derived by PCA methods are treated as damage-sensitive features. In this paper, the effective method of double-window PCA (DWPCA) and novel features are proposed for better damage identification

On-site estimation of multiple fault parameters has been performed in a rotor integrated with active-magnetic bearing (AMB) with a cracked shaft supported on flexible conventional bearings. In addition to external viscous damping (at flexible bearings), internal damping (at transverse crack) is considered to show its influence on the dynamics of the cracked system. The instability generated in the

In the paper, we solve two Stefan problems. The first problem recovers an unknown moving boundary by specifying the Cauchy boundary conditions on a fixed left-end. The second problem finds a time-dependent heat flux on the left-end, such that a desired moving boundary can be achieved. Then, we solve an inverse Cauchy-Stefan problem, using the over-specified Cauchy boundary conditions on a given moving

A new method for estimating the thermal properties of composite materials is proposed. It uses a previously developed thermal characterization method that is based on Karhunen–Loève decomposition (KLD) techniques in association with infrared thermography experiments or any other kind of experimental device providing dense data in spatial coordinates. The novelty of this work lies in the introduction

The approach is developed to specify a reconstruction of complicated functions using samples of limited size with invariant properties regarding the desired parameters. The idea is based on solutions to inverse problems, which should identify various representations of unknown parameters of a mathematical model and do so in a series. The sequential solutions to inverse problems ensure the identifiability

Large volume metrology is a key enabler of autonomous precision manufacturing. For component positioning, the optical-based metrology technique of photogrammetry could be used more widely if its accuracy was improved. These positional measurements are subject to uncertainties which can be greater than manufacturing tolerances. One source of uncertainty is due to thermal gradients, which cause the refraction

Fibre Bragg Gratings have become widespread measurement devices in engineering and other fields of application. In all but a few cases, the relation between cause and effect is simplified to a proportional model. However, at its mathematical core lies a nonlinear inverse problem which appears not to have received much attention in the literature. In this paper, we present this core problem to the mathematical

This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single direction of the incident plane wave. We propose a globally convergent convexification numerical algorithm to solve this nonlinear and ill-posed inverse problem. The key

Recently, an inverse design method called the ball spine algorithm (BSA) is introduced to design S-duct diffusers with elliptic cross-sections. The technique is developed for the 3-D design of S-shaped ducts with special cross-sectional profiles in the present work. The upper and lower lines of the S-duct symmetric section are modified under the BSA. Two types of special cross-section profiles are

Tall structures, during their service lifetime, face many scenarios and are often prone to damages. Generally, static or dynamic measurements from the entire structure are used while formulating the Structural Health Monitoring (SHM) techniques for damage diagnosis. In this paper, an output-only damage diagnostic technique using the decentralized concept (subdomain-based) for high-rise buildings, employing

In structural health monitoring, the localization of impact is one of the most basic and challenging problems. However, existing technologies are only suitable for obtaining the impact position of plate structures, which hinder their engineering applications. Here, we propose a new method to study the impact position of complex box structures. The proposed method is based on modal parameters and k-means

The nonlinear model has been developed and implemented to describe gas emission from coal slack placed in a sealed container (‘canister test’). The model accounts for initial gas content S, coefficients of diffusion D, mass transfer β and desorption kinetics γ, as well as for fractional composition of the sample. Using the developed analytical method of the initial boundary value problem solution,

Inverse problems are more challenging when only partial data are available in general. In this paper, we propose a two-step approach combining the extended sampling method and the ensemble Kalman filter to reconstruct an elastic rigid obstacle using partial data. In the first step, the approximate location of the unknown obstacle is obtained by the extended sampling method. In the second step, the

The aim of this paper is to retrieve the temperature-dependent refractive index distribution in parallel-plane semi-transparent media with combined conduction-radiation heat transfer, by the measurement of exit intensities over the boundaries. The finite volume method in combination with the discrete ordinates method is used to solve the energy equation. The results of the direct solution for both

Lightning location is a significant issue in the protection of transmission lines, renewable energy sources, and electrical equipment. In this article, a new technique for the determination of lightning striking points is been proposed. This method is depending on measured values of lightning-induced voltage obtained from distribution power lines in the vicinity of the lightning channel. The proposed

In this work, we prove the possibility of actively controlling the acoustic field in an ocean consisting of two homogeneous layers of constant depth using a surface source embedded in one of the layers. For a class of prescribed fields on some bounded control regions in either layer, we show the existence of a boundary input on the source, either acoustic pressure or normal velocity so that the propagated

Study of vehicle dynamics aggregates possibilities to enhance performance, safety and reliability, such as the integration of control systems, usually requiring knowledge on vehicle's states and parameters. However, some critical values are difficult to measure or are not disclosed. For this reason, dynamics and stability analysis of six-wheeled vehicles are compromised, and available information on

The change of electrodes’ conductivity is a crucial parameter during battery aging process, non-contact detection of battery electrodes’ defects through conductivity reconstruction is an innovative technology. In this paper, the magnetic induction tomography (MIT) was applied to reconstruct the conductivity of electrodes, the simplified battery models with complete and broken electrodes were chosen

We investigate a class of finite dimensional iteratively regularized Gauss–Newton methods for solving nonlinear irregular operator equations in a Hilbert space. The developed technique allows to investigate in a uniform style various discretization methods such as projection, quadrature and collocation schemes and to take into account available restrictions on the solution. We propose an a posteriori

Elastic Surface Algorithm (ESA), which was proposed for the inverse design in external flows, substitutes the airfoil wall by an elastic curved beam that deforms due to a difference between the target and current pressure distributions. The original ESA, such as all inverse design methods, which use only pressure as the target parameter, cannot converge in separated flows because of an almost constant

In this paper, we proposed a fractional diffusion model to simulate the movement of chloride in concrete. In such complex porous structure some of the free chlorides, which are affected by the surrounding heterogeneous physical environment, will be bounded physically and chemically. Furthermore, experiments reveal that the interesting heavy-tailed phenomena appear in diffusion process. The time and

In this paper, we study two identification problems related to the mud filtrate invasion phenomenon. We want to determine a parameter (the invasion rate) in the coefficients of the parabolic equation that describes the mud filtrate invasion phenomenon. In the first problem, we determine this parameter starting from the observed values of the mud filtrate dispersion. We reduce the problem to an optimal

In this paper, the inverse problem for identifying the initial value of time-fractional diffusion wave equation on spherically symmetric region is considered. The exact solution of this problem is obtained by using the method of separating variables and the property the Mittag–Leffler functions. This problem is ill-posed, i.e. the solution(if exists) does not depend on the measurable data. Three different

This study deals with the identification of source function from final time state observation in a two-dimensional hyperbolic problem. The solution to the direct problem is obtained by the weak solution approach and finite element method. In the part of the inverse problem, the trust-region method and Levenberg–Marquardt method, which are nonlinear least-squares optimization methods, are used for the

The undesired and unexpected closure of valves in pipelines is the most frequent failure that causes interruptions in the transport of natural gas. This work aims at the detection of valve closures by solving a state estimation problem with the Particle Filter method. The gas flow problem in the duct is solved with a Weighted Average Flux – Total Variation Diminishing scheme, while state variables

In this paper, we study an inverse transmission scattering problem of a time-harmonic acoustic wave from the viewpoint of Bayesian statistics. In Bayesian inversion, the solution of the inverse problem is the posterior distribution of the unknown parameters conditioned on the observational data. The shape of the scatterer will be reconstructed from full-aperture and limited-aperture far-field measurement

ABSTRACT Early detection of breast cancer will continue to be crucial in improving patient survival rates for the foreseeable future. Our long-term goal is to automate and refine the manual breast exam process using measured data on the breast surface in combination with formal inverse techniques to generate three-dimensional maps of the stiffness inside the breast tissue. In this paper, we report

Application of elasticity imaging inverse problem to identify Young's modulus in the elasticity problems in human's life is an interesting research area. In this study, we identify the modulus of elasticity for solving elasticity imaging inverse problem using a modified output least-squares method. Numerical convergence in the displacements of the direct problem for elasticity is investigated. To study

ABSTRACT This study considers an inverse problem, where the corresponding forward problem is given by a finite-dimensional linear operator T. The inverse problem has the following form: (data)=T(unknown). It is assumed that the number of patterns that the unknown quantity can take is finite. Then, even if Ker T≠{0}, the unknown quantity may be uniquely determined from the data. This case is the subject

ABSTRACT Constructing a matrix by its spectral information including singular values is called inverse singular value problem (ISVP). In this paper, an ISVP for nonsymmetric ahead arrow matrix by two eigenpairs of the required matrix and one singular value of each leading principal submatrices is investigated. To solve the problem, the recurrence relation of characteristic polynomial of the block Jordan–Weilant

ABSTRACT In this article, we consider an inverse source problem for Poisson equation in a strip domain. That is to determine source term in the Poisson equation from a noisy boundary data. This is an ill-posed problem in the sense of Hadamard, i.e., small changes in the data can cause arbitrarily large changes in the results. Before we give the main results about our proposed problem, we display some

In this paper, the problem of unknown source identification for the space-time fractional diffusion equation is studied. In this equation, the time fractional derivative used is a new fractional derivative, namely, Caputo-Fabrizio fractional derivative. We have illustrated that this problem is an ill-posed problem. Under the assumption of a priori bound, we obtain the optimal error bound analysis of

Achieving complete data of measured mode shapes is costly during the process of structural dynamic test. This results in a challenge for the damage detection. This paper concentrates on structural damage detection problem with incomplete mode shape data. An efficient method to deal with this problem is proposed. The generalized flexibility matrix (GFM) is employed. By introducing a few new variables

In this paper, we consider the inverse source problem of heat conduction equation with time-dependent diffusivity on a spherical symmetric domain. This problem is ill-posed, i.e. the solution of the problem does not depend continuously on the measured data. To solve this problem, we propose an iterative regularization method and obtain the Hölder type error estimates. Numerical examples are presented

This work is focused on the transient analysis of a haemodialyser. The objective is to sequentially estimate the concentration of creatinine in the blood returning to the patient, by solving a state estimation problem with measurements of the outflow creatinine concentration in the dialysate. Simulated measurements containing Gaussian errors were used in the inverse analysis, which was based on the

Goal of this elaboration is to investigate the mathematical model of the inverse problem of binary alloy solidification within the casting mould, with the material shrinkage and the macrosegregation phenomena included simultaneously. Major result of this paper is the solution of the inverse problem consisting in reconstruction of the following elements: the thermal resistance of the air gap created

ABSTRACT Achieving a unique solution for the 3D inverse design of a curved duct is a challenging problem in aerodynamic design. The centre-line curvature, and cross-sections’ area and shape of a 3D curved duct influence the wall pressure distribution. All the previous developments on the ball-spine method were limited to 2D and quasi-3D ducts, in which only the upper and lower lines of the symmetry

In this work, two-dimensional inverse quasi-linear parabolic problem with periodic boundary and integral overdetermination conditions is investigated. The formal solution is obtained by the Fourier approximation. Under some natural regularity and consistency conditions on the input data,the existence, uniqueness and continuously dependence upon the data of the solution are proved by iteration method

ABSTRACT Urea-hydrolysing biofilms are crucial to applications in medicine, engineering, and science. Quantitative information about ureolysis rates in biofilms is required to model these applications. We formulate a novel model of urea consumption in a biofilm that allows different kinetics, for example either first order or Michaelis–Menten. The model is fit to synthetic data to validate and compare

This work advances the approximation error model approach for the inverse analysis of the biodiesel synthesis using soybean oil and methanol in 3D-microreactors. Two hybrid numerical-analytical approaches of reduced computational cost are considered to offer an approximate forward problem solution for a three-dimensional nonlinear coupled diffusive-convective-reactive model. First, the Generalized

In this research work, a crack diagnosis method for beam-column structures is proposed considering axial load effects through experimental data. The proposed method is employed for the detection of damage locations including single and multiple damage scenarios considering four cases of simply supported beam-column. The results show that the locations of single and multiple damage scenarios can be

ABSTRACT This work is devoted to studying a direct and inverse scattering problem for a magnetoelastic layer having a defect, in the frame of the electromagnetic theory. In terms of the displacement field over the defect's contour, a coupled system of boundary integral equations is formulated, for magnetically permeable and impermeable defects. To identify the position and size of the defect, an efficient

This paper investigates the approximate solutions to the time-dependent acoustic scattering problem with a point-like scatterer under some basic assumptions and provides a simple method to reconstruct the location of the scatterer. The approximations of the solution to the forward scattering problem are analysed utilizing Green's function and the retarded single-layer potential. Then, based on the

A discrete gyroscopic system is characterized by 2 n first-order ordinary differential equations defined by one symmetric and one skew-symmetric, which system describes the motion of a spinning body containing elastic parts. In this paper, we consider the inverse problems of such system: Given partial spectral data, find a system such that it is of the desired spectral data. The general solution of

ABSTRACT Among the most significant challenges with using Markov chain Monte Carlo (MCMC) methods for sampling from the posterior distributions of Bayesian inverse problems is the rate at which the sampling becomes computationally intractable, as a function of the number of estimated parameters. In image deblurring, there are many MCMC algorithms in the literature, but few attempt reconstructions for

ABSTRACT The structured partial quadratic inverse eigenvalue problem (SPQIEP) is to construct the structured quadratic matrix polynomial using the partial eigendata. The structures arising in physical applications include symmetry, band (tridiagonal, diagonal, pentagonal) etc. The construction of the structured matrix polynomial is the most difficult aspect of this problem and the research on structured

ABSTRACT Among the most significant challenges with using Markov chain Monte Carlo (MCMC) methods for sampling from the posterior distributions of Bayesian inverse problems is the rate at which the sampling becomes computationally intractable, as a function of the number of estimated parameters. In image deblurring, there are many MCMC algorithms in the literature, but few attempt reconstructions for

Intravascular photoacoustic tomography (IVPAT) is a newly developed imaging modality for the diagnosis and intervention of coronary artery diseases. It is an ill-posed nonlinear least squares (NLS) problem to recover the absorbed optical energy density (AOED) and optical absorption coefficient (OAC) distribution in the vascular cross sections from pressure photoacoustically generated by tissues with

(2021). Foreword. Inverse Problems in Science and Engineering: Vol. 29, No. 1, pp. 1-1.

ABSTRACT This paper deals with the quantification of the different rates in epidemiological models from a function estimation framework, with the objective of identifying the desired unknowns without defining a priori basis functions for describing its behaviour. This approach is used to analyze data for the Covid-19 pandemic in Italy and Brazil. The forward problem is written in terms of the SIRD

Two efficient methods are presented to detect multiple cracks in 2D elastic bodies, based on the insights from Extended Finite Element. Adetection mesh is assigned to the cracked body and the responses are measured at the nodes. A finite element model with the same mesh is used to represent the uncracked state of the physical body. In the first method which is called Crack Detection based on Residual

This study presents the free vibration analysis of a double tapered beam having linearly varying both thickness and width, by using finite element and component mode synthesis methods. To determine the natural frequency and mode shape of the double tapered cracked beam, the stiffness and mass matrices of the beam have been obtained. The crack in the beam is modeled as a massless spring, and the beam

Mechanical parameters of rock mass are essential in rock engineering for stability analysis, supporting design, and safety construction. The inverse analysis has been commonly used in rock engineering to determine the mechanical parameters of the rock mass. In this study, a novel inverse analysis approach was proposed through combing high dimensional model representation (HDMR), Excel solver, and numerical

Optimal continuous-discrete filtering for a nonlinear system requires evolving the forward Kolmogorov equation, that is a Fokker–Planck equation, in alternation with Bayes' conditional updating. We present two numerical grid-methods that represent density functions on a mesh, or grid. For low-dimensional, smooth systems the finite-volume method is an effective solver that gives estimates that converge

Optimal continuous-discrete filtering for a nonlinear system requires evolving the forward Kolmogorov equation, that is a Fokker–Planck equation, in alternation with Bayes' conditional updating. We present two numerical grid-methods that represent density functions on a mesh, or grid. For low-dimensional, smooth systems the finite-volume method is an effective solver that gives estimates that converge

In the present work, we investigate the inverse problem of identifying simultaneously the denoised image and the weighting parameter that controls the balance between two diffusion operators for an evolutionary partial differential equation (PDE). The problem is formulated as a non-smooth PDE-constrained optimization model. This PDE is constructed by second- and fourth-order diffusive tensors that

The present work presents a model for nonlocal and viscoelastic Euler-Bernoulli beams and aspects of its calibration are addressed. The nonlocal feature of the model is described by the nonlocal elasticity theory proposed by Eringen and its viscoelastic behaviour is modelled by means of internal variables. Parametric analyses are performed to determine the impact of the nonlocal and viscoelastic parameters

In this paper, we present a method of choice of an adaptative regularization parameter for data corrupted by Poisson noise based on a bilevel approach. The forward operator considered is nonlinear. The existence and unicity of the smoothed lower level problem, the differentiability properties of the constraint, and the adjoint method used to calculate the gradient of the reduced functional are studied