(2021). Foreword. Inverse Problems in Science and Engineering. Ahead of Print.

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

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

This article is devoted to applying a local meshless method for specifying an unknown control parameter in one- and multi-dimensional inverse problems which are considered with a temperature overspecification condition at a specific point or an energy overspecification condition over the computational domain. Finding the unknowns in inverse problems is a challenge because these problems are modeled

ABSTRACT Fuzzy inference method is applied to formulate an algorithm capable of estimating material elastic constants (ECs) of a specimen by solving an inverse problem with a group of measured resonance frequencies obtained via Resonant Ultrasound Spectroscopy (RUS). The algorithm is validated with RUS data from a specimen of polycrystalline aluminium alloy. Then the algorithm is found to be sensitive

ABSTRACT The paper deals with the identification of multiple unknown time-dependent point sources occurring in 3D dispersion–advection–reaction equations. Based on the developed appropriate adjoint functions, we establish a constructive identifiability result depending on the flow nature that yields guidelines leading to a quasi-direct detection–identification method. In practice, assuming to be available

The total variation minimization is proposed for use in recovering the mass density of a fluid medium from back-scattered acoustic waves by the dynamical version of the boundary control method. This may be of particular interest to underwater acoustic imaging or ultrasound tomography. In particular, an analogue of the regularized mean curvature flow equation is proposed and developed to obtain numerical

ABSTRACT The properties of complex particle systems typically depend on multivariate distributions of particle properties, like size and shape characteristics. Multidimensional particle property distributions can be a powerful tool to describe these systems. However, only few techniques exist which are able to simultaneously measure more than one property of individual particles in fast and efficient

Fractional derivative is an important notion in the study of the contemporary mathematics not only because it is more mathematically general than the classical derivative but also it really has applications to understand many physical phenomena. In particular, fractional derivatives are related to long power-law particle jumps, which can be understood as transient anomalous sub-diffusion model (see

ABSTRACT In this article, we will find centrosymmetric matrix solutions A of the left and right inverse eigenvalue problem under a submatrix A 0 constraint, where A 0 is also a centrosymmetric matrix. In other words, expand the system (matrix) A from the centre subsystem (submatrix) A 0 satisfying the matrix constraint, where A and A 0 are both centrosymmetric matrices. Using the similar structure

ABSTRACT We proved the unique determination of the variable order in a two-scale mobile–immobile variable-order time-fractional partial differential equation with a variable diffusivity tensor imposed on a general multi-dimensional domain, with the observations of the unknown solutions on any arbitrarily small spatial domain over a sufficiently small time interval. The proved theorem provides a guidance

ABSTRACT This paper presents a numerical study of an augmented Kalman filter extended with a fixed-lag smoother. The smoother solves the joint input and state estimation problem based on sparse vibration measurements. Two numerical examples are examined in order to study the influence of model errors and measurement noise on the estimate quality. From simulations of a simply supported beam, it is shown

Face recognition approaches that use subspace projection are heavily related to basis images, especially in the case of partial occlusion. To improve the recognition performance, the occlusion should be excluded from the test image during the recognition process. In terms of similarity with image reconstruction, the proposed approach aims at representing the whole face image based on facial subregion

ABSTRACT The time conformable heat equation is a generalization of classical heat equation involved local and limit-based derivative, which is called conformable fractional derivative. In this paper, we study a backward problem for the time conformable fractional heat equation defined in cylindrical coordinates for the axis-symmetric case which is a severely ill-posed problem. By using a modified quasi-boundary

In this paper, a second order differential pencil, namely diffusion equation with Dirichlet boundary conditions which includes conformable fractional derivatives of order α ( 0 < α ≤ 1 ) instead of the ordinary derivatives in a traditional diffusion operator, is considered. Firstly, the asymptotic formulae of eigenvalues and eigenfunctions of the operator are obtained. Secondly, the nodal points which

ABSTRACT In this paper for the first time, a numerical code based on Levenberg–Marquardt method is presented for solving inverse heat transfer problem of axisymmetric stagnation flow impinging on a cylinder with uniform transpiration and to estimate the time-dependent heat flux using temperature distribution at a point. k ¯ The effect of noisy data on the final result is studied. The maximum value

ABSTRACT A solution method for an inverse problem of determining the time-dependent lowest order coefficient of the 2D bioheat Pennes equation with nonlocal boundary conditions and total energy integral overdetermination condition recently appeared in literature is analysed and improved. Improvements include convective boundary condition into the model, the development of an accurate forward solver

Appropriate regularization parameter specification is the linchpin for solving ill-posed inverse problems when regularization method is applied. This paper presents a novel technique to determine cut off singular values in the truncated singular value decomposition (TSVD) methods. Simple formulae are presented to calculate the index number of the singular value, beyond which all the smaller singular

ABSTRACT This work is concerned with the image reconstruction of the Jacobian-based linearized EIT problem. Based on the homotopy perturbation technology, we first propose a novel class of iteration schemes with different orders of approximation truncation (named as HPI for short), which contains Landweber-type iteration method. Afterwards, nonsmooth priors such as ℓ 1 -norm or total variation penalty

We are concerned with the inverse spectral problem for a quadratic pencil operator. We show that one given spectrum is enough for its reconstruction in the case of one analytic potential. To do so we first prove few identities between the Taylor coefficients of the sought function and the Taylor coefficients of the characteristic function of the operator, whose zeros are the given eigenvalues. The

This work is to investigate the image reconstruction of electrical impedance tomography from the electrical measurements made on an object's surface. An ℓ p -norm (0

In this article, for a degenerate parabolic equation we study an inverse problem for restoration of source temperature from the information of final temperature profile. The uniqueness of this inverse problem is first established by taking an integral transform and using Liouville's theorem (complex analysis). With aids of an integral identity, a Lipschitz stability for the inverse problem is further

We study the three-dimensional inverse problem of elastography, that is finding the Young's modulus of a biological tissue from known values of its vertical displacements. In this way, one can find inclusions with Young's modulus several times higher than its known background value. Such inclusions are interpreted as tumours. A quasistatic statement of the problem is used in which the fragment of the

This work presents moving load identification on Euler-Bernoulli beams with viscoelastic boundary conditions based on beam acceleration responses. The Tikhonov regularization and generalized cross validation (GCV) methods are used to investigate the performances of different regularization matrices (L matrices) in terms of their effectiveness in reducing errors in load identification. The effects from

Compton scattering describes the scattering of a photon after its collision with an electron. The recent developments of spectral cameras, able to collect photons in terms of energy, open the way to a new imaging concept: 3D Compton scattering imaging (CSI), which seeks to exploit the scattered radiation as a vector of information while a specimen of interest is illuminated by a monochromatic ionizing

In this paper, we consider a problem of recovering a space-dependent source for a time fractional diffusion wave equation by the fractional Landweber method. The inverse problem has been transformed into an integral equation by using the final measured data. We use the fractional Landweber regularization method for overcoming the ill-posedness. We discuss an a-priori regularization parameter choice

When there exists fuzzy uncertainty in experimentally determined information, viscoelastic constitutive parameters to be identified are treated as fuzzy variables, and a two-stage strategy cooperating with particle swarm method is presented to identify membership functions of fuzzy parameters. At each stage, inverse fuzzy problem is formulated as a series of α-level strategy-based inverse interval

We solve the inverse Cauchy problem of elliptic type partial differential equations in an arbitrary 3D closed walled shell for recovering unknown data on an inner surface, with the over-specified Cauchy boundary conditions given on an outer surface. We first derive a homogenization function in the 3D domain to annihilate the Dirichlet as well as the Neumann data on the outer surface. Then, we can transform

The aim of this paper is to identify numerically the timewise thermal conductivity coefficients in the two-dimensional heat equation in a rectangular domain using initial and Dirichlet boundary conditions and the local heat flux as over-specification conditions. The measurement data represented by the local heat flux is shown to ensure the unique solvability of the inverse problem solution. The two-dimensional

This paper presents a novel approach for detecting damage in a cable-stayed bridge based on adaptive signal processing and feature extraction. The Empirical Mode Decomposition (EMD) technique is employed in this research to obtain the Intrinsic Mode Functions (IMFs). Several features in time and frequency domains are extracted from IMFs as damage-sensitive features. Next, to reduce false alarms, several

A three-dimensional shape design problem is considered to determine the optimal snowflake-shaped fins (SSF), based on the minimization of maximum domain temperature of fin. The Levenberg-Marquardt method (LMM) and software package CFD-ACE+ are used as the design tools. The SSF can be obtained by modifying the helm-shaped fins (HSF), the fine surfaces of HSF can be increased by splitting central part

This paper proposes a new non-destructive method to reconstruct the distribution of residual stresses around notches from the measured displacements under external loads. For this purpose, a linear finite element method based on the Willis-form equations is firstly established to calculate the displacements, so that they explicitly contain the impact of the gradient of residual stresses, which can

The connection of different modifications of the method of linear integral representation is studied. Solutions of the related inverse problems based upon a ‘hybrid version of two approximations’ of the topography and geopotential fields enable more refined tuning of the method in solving the inverse problems of geophysics and geomorphology and more complete allowance for the a priori information about

An inverse method to estimate the discharge of rivers observed by satellite altimetry is developed and assessed. The flow model relies on the Saint-Venant equations combined with a dedicated algebraic system. The resulting hierarchical flow model combined with variational data assimilation enables estimation of the key unknown flow features: the discharge Q(x,t), an effective bathymetry b(x) and friction

Measurements of alternating current potential drop at the surface of a conductor can be predicted based on knowledge of the electromagnetic material properties of the conductor and their variation with position. Here we consider the inverse problem of finding the variations of the material properties with depth from multi-frequency potential drop data, which are generated by injecting alternating currents

In this paper, we present a method to reconstruct the spatially varying conductivity tensor in isotropic and orthotropic materials, involved in a two-dimensional transient anisotropic model with Robin boundary conditions. For the reconstruction, the partial differential equation is solved by a semi-discrete method that combines a pseudospectral collocation method for spatial variables and Crank–Nicolson

This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front surfaces of objects buried very closely under the ground. These objects mimic explosives, like, e.g. antipersonnel land mines and improvised explosive devices. We

New method of scanning tomography of subsurface dielectric inhomogeneities by bistatic measurements of 2D distributions of the scattered signal with the variable source-receiver offset (base) is considered. This method is based on the solution of the corresponding inverse scattering problem – retrieval of 3D distribution of complex permittivity of inhomogeneities from the solution of 3D integral equation

In this paper, a non-linear parameter identification method for structures is presented, whereby the instantaneous power flow balance of the substructure of interest is enforced. The time-domain power flow into the non-linear substructure is balanced against the power transmitted to adjacent structures, damping and kinetic and strain energies. Enforcing this condition of matching the net power balance

Inverse estimation of the temperature/phase change-dependent refractive index of semitransparent media is studied in present work. The direct models (including the coupled radiation-conduction heat transfer and coupled radiation-phase change heat transfer exposed to the laser irradiation) are solved by the finite volume method. The inverse model adopts stochastic particle swarm optimization (SPSO)

An inverse source problem for an n-dimensional heat equation with a time-varying coefficient is investigated. The spatially dependent component of a source function is determined from a measurement at the final time. The inverse problem is regularized by a mollification method. Hölder-type stability estimates are proved. Error estimates of Hölder type are also proved for regularized solutions for both

Inverse problems are of importance in many fields of science and engineering. Electromagnetic inversion deals with estimating information contained in electromagnetic measurements. The inversion scheme needs to be designed properly to compensate for Gibbs oscillations effects in the solution, and hence give better validation for the estimated quantities. In this paper an inversion methodology based

The main mathematical results on the data processing in vibrational spectroscopy are presented. The approaches and algorithms proposed for molecular force field calculations have been constructed on a base of regularizing methods for solving nonlinear ill-posed problems and have been implemented in the software package SPECTRUM. These algorithms were used for constructing the regularized ab initio

We consider the problem of guaranteed estimation of unknown right-hand sides of the equations entering the statement of the exterior Neumann problems for the Helmholtz equation from indirect observations of their solutions. A method is developed for the determination of guaranteed a posteriori estimates of this right-hand sides which are compatible with measurement data. It is shown that such estimates

Support vector machine (SVM) is regarded as one of the most effective techniques for supervised learning, while the Gaussian kernel SVM is widely utilized due to its excellent performance capabilities. To ensure high performance of models, hyperparameters, i.e. kernel width and penalty factor must be determined appropriately. This paper studies the influence of hyperparameters on the Gaussian kernel

This paper proposes a new regularization technique using spectral graph wavelet for backward heat conduction problem (BHCP) on the graph. The method uses the fourth-order compact difference for an approximation of differential operators. Meanwhile, the error estimate between the exact and wavelet regularized solution is derived. Adaptive node arrangement is obtained using spectral graph wavelet. The

In this paper, we propose a novel reconstruction scheme for the low-frequency near-field electromagnetic imaging of high-contrast conductivity distributions inside shielded regions using the system of Maxwell's equations in 3D. In our novel scheme, we focus on estimating the shape characteristics of the electrical conductivity profile inside these regions from low-frequency electromagnetic data measured

In this paper, we consider the inverse problem of recovering an isotropic elastic tensor from the Neumann-to-Dirichlet map. To this end, we prove a Lipschitz stability estimate for Lamé parameters with certain regularity assumptions. In addition, we assume that the Lamé parameters belong to a known finite subspace with a priori known bounds and that they fulfil a monotonicity property. The proof relies

In previous work the author presented a novel method whereby relative values of the specific heat capacity and thermal conductivity of a composite rod may be accurately estimated by analyzing oscillations present within eigenvalue spectra. This work described how the solotone effect may be utilized to solve a parameter estimation inverse problem. In this paper, we show how the solotone inverse method

The knowledge of the variation of arc current is helpful in improving the breaking performance of a vacuum circuit breaker. As a novel non-intrusive method, arc magnetic performance testing technology has attracted attention. In view of the widely used regularization method of the standard form in arc current reconstructions cannot fully overcome the ill-posed nature of the Biot-Savart equation, the

In this paper we consider the identification of the initial condition for a distributed order diffusion equation. We first prove the unique existence and the regularity properties of the strong solution on the bounded temporal-spacial domain based on the eigenfunction expansions. The ill-posedness of the backward problem is interpreted by the compactness of the observation operator. Next the Laplace

New exact solutions for unidirectional unsteady flows of incompressible viscous fluids with linear dependence of viscosity on the pressure between two infinite horizontal parallel plates are established when the lower plate is moving in its plane with an arbitrary time-dependent velocity. In addition to being useful solutions to idealizations of technologically relevant problems such exact solutions

Seismic inversion is an effective way to get stress distribution of rock in coal mine, but its usage is still limited by multi-solution problem in practice. As seismometers can only be deployed in limited areas in underground coal mine, it is impossible to solve multi-solution problem by adding more seismometers, thus, we propose a new seismic inversion method which introduces stress value changes

We developed a method of inverse problem solving in semiconductor photoacoustics based on neural networks application. Simple structured neural networks, trained on a large set of data obtained by the well – known theoretical models in the 20 Hz–20 kHz modulation frequency range, are applied to determine thermal diffusivity, coefficient of linear expansion and thickness of n – type silicon samples