A method for the path synthesis of a planar five-bar mechanism based on wavelet analysis theory is proposed in this paper. Wavelet transform analysis is used to extract wavelet characteristic parameters(WCPs) from the basic dimensional types(BDTs) database. Combined the numerical atlas method with multidimensional search tree, a four dimensions search tree with a depth of five is obtained, in which

This paper is devoted to investigating a two-dimensional inverse anomalous diffusion problem. The missing solely time-dependent Dirichlet boundary condition is recovered by imposing an additional integral measurement over the domain. An efficient computational technique based on a combination of a time integration scheme and local meshless Petrov–Galerkin method is implemented to solve the governing

(2020). Celebration of 90th birthday of James Vere Beck. Inverse Problems in Science and Engineering: Vol. 28, No. 5, pp. 599-600.

In this paper, the bi-Helmholtz equation with Cauchy conditions is nominated in a n-dimensional strip domain. It is shown that this Cauchy problem may be ill-posed in the sense of Hadamard. In order to overcome the ill-posedness, a suitable regularization method has to be applied to the Cauchy problem. Hence, two well-known wavelet and Fourier regularization methods are used for solving this ill-posed

We discuss inverse problems to finding the time-dependent coefficient for the multidimensional Cauchy problems for both strictly hyperbolic equations and polyharmonic heat equations. We also extend our techniques to the general inverse Cauchy problems for evolution equations.

Electrical impedance tomography (EIT) is a boundary measurement inverse technique targeting reconstruction of the conductivity distribution of the interior of a physical body based on boundary measurement data. Typically, the measured data are uncertain because of various error sources; thus, there are many uncertainties in the reconstructed image. This study attempts to quantify the effects of these

In this paper, the dynamic reliability and global sensitivity analysis method of double random vibration system is proposed, considering structure uncertainty and excitation uncertainty of complex mechanical and structural systems under random load. Based on the Miner criterion of fatigue failure of structures, the dynamic responses of structures under the condition of double random vibration are analyzed

In this paper, we consider the two-dimensional Fredholm integral equation of the first kind. The kernel of this equation models the scattering of a laser beam by spheroids having the same fixed orientation. The unknown function under the integral describes the distribution of spheroids along two semi-axes. The input data are the diffraction pattern corresponding to the scattering of the laser beam

In this paper, we combine the maximum entropy principle with binomial tree to construct a non-recombining entropy binomial tree pricing model under the volatility that is a function of time, and give the rate of convergence. The model may yield an unbiased and objective probability. In addition, we research the calibration problem of volatility with the entropy binomial tree, and adopt an exterior

We consider the problem of computing the initial condition for a general parabolic equation from the Cauchy lateral data. The stability of this problem is well-known to be logarithmic. In this paper, we introduce an approximate model, as a coupled linear system of elliptic partial differential equations. Solution to this model is the vector of Fourier coefficients of the solutions to the parabolic

Ultrasound Tomography (UT) is primarily used for the detection of malignant tissue in the human breast. However, the reconstruction algorithms used for UT require large computational time and are based upon solving a nonlinear, ill-posed inverse problem. We constructed and solved the inverse scattering problem from UT using the Distorted Born Iterative method. Since this problem is ill-posed, this

In this paper, we have developed the spectral theory for a conformable fractional Sturm-Liouville problem Lα(q(x),h,H) with boundary conditions which include conformable fractional derivatives of order α, 0<α⩽1, and prove a completeness theorem and an expansion theorem. We obtain the canonical infinite product constructed by the zero set of the characteristic function of Lα. Also, we calculate the

The Dirac system with an integral delay in the form of convolution is considered. We suppose that the convolution kernel, having four independent components, is known a priori on a part of the interval. A partial inverse problem is studied, which consists in recovering the kernel on the remaining part of the interval from some fractional parts of two spectra. Uniqueness theorems are proved, and a constructive

This study newly demonstrates a compressed sensing (CS)-based reconstruction scheme for computed tomography (CT) with a translational trajectory. CT with a translational trajectory has many potential applications in the field of non-destructive testing (NDT) and medicine. For example, in the X-ray inspection of a large civil engineering structure, the movements of the source and detector are strictly

This paper deals with the reconstruction of small-amplitude perturbations in the electric properties (permittivity and conductivity) of a medium from boundary measurements of the electric field at a fixed frequency. The underlying model is the three-dimensional time-harmonic Maxwell equations in the electric field. Sensitivity analysis with respect to the parameters is performed, and explicit relations

An inverse microtomography problem is under consideration in a class of functions with bounded V H variation. An algorithm for solving this problem is proposed based on Tikhonov's regularization with a special regularizer. The algorithm ensures piecewise uniform convergence of approximate solutions to exact solution of the inverse problem. In addition, the question of a-posteriori error estimate of

An inverse spectral problem is studied for the matrix Sturm–Liouville operator on a finite interval with the general self-adjoint boundary condition. We obtain a constructive solution based on the method of spectral mappings for the considered inverse problem. The nonlinear inverse problem is reduced to a linear equation in a special Banach space of infinite matrix sequences. In addition, we apply

The monotonicity method for the inverse acoustic scattering problem is to understand the inclusion relation between an unknown object and artificial one by comparing the far field operator with the artificial operator. This paper introduces the development of this method to the inverse crack scattering problem. Our aim is to give the following two indicators: One (Theorem 1.1) is to determine whether

The AISI 304 stainless steel has largely been used in industry owing to its good formability characteristics. Therefore, the use of proper material parameters is essential for a successful numerical simulation of forming operations. Within this framework, this work addresses a parameter identification strategy using strategies based on multiple mechanical tests – a multi-test optimization scheme. The

This paper concerns a one-phase inverse Stefan problem in one-dimensional space. The problem is ill-posed in the sense that the solution does not depend continuously on the data. We also consider noisy data for this problem. As such, we first regularize the proposed problem by the discrete mollification method. We apply the integration matrix using Bernstein basis polynomials for the discrete mollification

Tikhonov regularization is an usual method to solve an ill-posed problem, recommended when the input data are contaminated with noise. However, in some cases, the use of this technique is not sufficient to provide good solutions. In this work, an improvement of the Tikhonov regularization method was proposed and tested in the inverse black body radiation problem. The method proposed consisted in including

Several alternatives have been proposed to model the radiation profile emitted by flames. Among them there is the weighted-multi-point-source-model (WMP), which is able to provide good predictions for medium and far distances. Despite being a simple model, the determination of its parameters can be difficult, which creates the opportunity to apply optimisation methods in order to find the best answer

The unloaded configuration of a body without residual stresses is generally used as the starting point to compute the displacement field but may be unknown for some applications. In this paper, we propose a novel inverse formulation to identify the unloaded configuration of a deformed hyperelastic body using finite element based discretization schemes. The inverse problem consists of finding a domain

An algorithm for the reconstruction of a symmetric matrix from the eigenvalues of finite dimensional perturbations is given. The sufficient condition of determining the finite symmetric matrices is derived.

The scalar problem of reconstruction of an unknown refractive index of an inhomogeneous solid is considered. The original boundary value problem for the Helmholtz equation with an unknown refractive index is reduced to the source-type integral equation. The solution to the inverse problem is obtained in two steps. First, the integral equation of the first kind is solved in the inhomogeneity domain

This paper studies an inverse problem of recovering an unknown diffusion coefficient in a parabolic equation. We adopt a total variation regularization method to deal with the ill-posedness. This method has the advantage to solve problems that the solution is non-smooth or discontinuous. By transforming the problem into an optimal control problem, we derive a necessary condition of the control functional

This paper presents a new class of the equation error estimator using de-noised displacement by the temporal–spatial filter for the system identification in an elastic solid. The finite element method is employed to discretize the equation of motion for an elastic solid, and the Young’s modulus of each finite element is estimated by the proposed approach. The temporal–spatial filter is applied to de-noise

In this work, we study the reconstruction of blood velocity with contrast enhanced computed tomography with tomographic projections perpendicular to the main flow field direction. The inverse problem is regularized with a convection-diffusion partial differential equation and with the Navier-Stokes equation. The velocity field is reconstructed together with the density field with a first-order adjoint

Under the condition of extremely under-sampling, the iterative algorithm based on the total variation(TV) constrain is common for the reconstruction of optical deflection tomography. In the algorithm, the minimization of TV is implemented by the gradient descent approach, and the constraints are performed by projection on convex sets (POCS). In this paper, we discuss the modulation factor of the gradient

This study proposes the use of artificial neural network (ANN) based surrogate framework along with simulated annealing (SA) approach to inversely estimate the optimum values of heat source control parameters in a heat treatment furnace. In particular, a two-dimensional radiant furnace with gas fired heaters has been considered and the heat source control parameters for a general gaussian heating profile

This paper deals with the solution of an inverse problem for the heat equation aimed at nondestructive evaluation of fractures, emerging on the accessible surface of a slab, by means of Active Thermography. In real life, this surface is heated with a laser and its temperature is measured for a time interval by means of an infrared camera. A fundamental step in iterative inversion methods is the numerical

In the paper, we solve a non-homogeneous heat conduction equation with non-homogeneous boundary conditions in a 2D rectangle. First, we derive the domain/boundary integral equations for both the forward and backward heat conduction problems. Then, by using the technique of homogenization, inserting the adjoint Trefftz test functions into the derived integral equations and expanding the solutions in

In this study, we aimed to describe a modern, efficient, and reproducible methodology to optimize respiration rate parameters coupled with transport properties in mass balances describing Modified atmosphere packaging (MAP) systems. We considered mass balances for three different respiration rate j film (exponential, competitive and uncompetitive Michaelis–Menten kinetics) coupled with transport properties

We develop a generalized Newton scheme called IHNC (inverse hypernetted-chain iteration) for the construction of effective pair potentials for systems of interacting point-like particles. The construction is realized in such a way that the distribution of the particles matches a given radial distribution function. The IHNC iteration uses the hypernetted-chain integral equation for an approximate evaluation

Restoring images corrupted by Poisson noise have attracted much attention in recent years due to its significant applications in image processing. There are various regularization methods of solving this problem and one of the most famous is the total variation (TV) model. In this paper, we present a new method based on accelerated alternating minimization algorithm (AAMA) which involves minimizing

We consider the inverse problem of estimating the spatially varying pulse wave velocity in blood vessels in the brain from dynamic MRI data, as it appears in the recently proposed imaging technique of Magnetic Resonance Advection Imaging (MRAI). The problem is formulated as a linear operator equation with a noisy operator and solved using a conjugate gradient-type approach. Numerical examples on experimental

The problem of reconstructing a matrix with a specific structure from a partial or total spectral data is known as inverse eigenvalue problem which arises in a variety of applications. In this paper, we study a partially described inverse eigenvalue problem of periodic Jacobi matrices and prove some spectral properties of such matrices. The problem involves the reconstruction of the matrix by one eigenvalue

This article is concerned with solving nonlinear inverse problems to recover the second-order nonlinear Sturm–Liouville operators, probably including a nonlinear convective term, which refers to over-specified boundary data. Utilising a homogenization approach with the boundary data, a series of boundary functions are obtained and consist of a linear space combined with the zero element. The energetic

In this paper, an inverse Schrödinger problem of potential-free field is studied. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. Based on an a priori assumption, the optimal errorbound analysis is given. Moreover, two different regularization methods are used to solve this problem, respectively. Under an a priori and an a posteriori regularization

This paper proposes a model-based approach for identifying rotordynamic parameters using full spectrum. First, for developing a mathematical model a cracked shaft system with an offset-disc integrated with an active magnetic bearing (AMB) is considered. Moreover, external viscous and internal (rotating) damping is considered in the mathematical model to analyze their effect on the dynamics of the cracked

This paper addresses the development of an inversion scheme based on Markov Chain Monte Carlo integrating process modelling with monitoring data for the real-time probabilistic estimation of unknown stochastic input parameters such as heat transfer coefficient and resin thermal conductivity and process outcomes during the manufacture of fibrous composites materials. Kriging was utilized to build an

This paper constructs an unconditionally stable explicit finite difference scheme, marching backward in time, that can solve an interesting but limited class of ill-posed, time-reversed, 2D incompressible Navier–Stokes initial value problems. Stability is achieved by applying a compensating smoothing operator at each time step to quench the instability. This leads to a distortion away from the true

This paper is concerned with a reconstruction method for multiple moving point/dipole wave sources. We assume that the number, locations, and magnitudes/moments of wave sources are unknown and consider the problem to reconstruct these parameters from the measurement of the wave field on the boundary. For this problem, we derive algebraic relations between the parameters of wave sources and the reciprocity

In this paper, a new method is used based on polynomials equipped with a parameter to solve two parabolic inverse problems. These inverse problems have nonlocal boundary conditions and over-determination of data that make it difficult to solve these problems. In this method, we use the combination of the finite difference method and the finite element method. In each point tj, a nonlinear equation

In this paper, a method is implemented to a one-dimensional inverse problem with a parabolic differential equation of fractional order in which the fractional derivative is in the Caputo sense. The considered inverse problem involves a time-dependent source control parameter p(t). In order to numerically solve the problem, first, the main problem is converted to a homogeneous problem by Lagrange interpolation

Intermittent spray cooling (ISC) is an active flow control technique that is used to provide rapid response and increase the spray efficiency. The transient feature of surface heat flux and temperature is important for the understanding of ISC performance. It is also a sensitive parameter in the implementation of the control strategy of ISC. In this study, a sequential-function-specification method

In this paper we consider the interior inverse problem of identifying a rigid boundary of an annular infinitely long cylinder within which there is a stationary Oseen viscous fluid, by measuring various quantities such as the fluid velocity, fluid traction (stress force) and/or the pressure gradient on portions of the outer accessible boundary of the annular geometry. The inverse problems are nonlinear

An inverted fin shape design problem in determining the optimal geometry of wavy-shapes inverted fins in a two-dimensional domain, based on the desired cooling tool average temperature and cooling tool area, is examined in this work. The commercial software CFD-ACE+ and Levenberg-Marquardt method (LMM) are utilized as the design tools. The numerical experiments are performed to verify the validity

The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper, we investigate this issue for the sparse data problem in photoacoustic tomography (PAT). We develop a direct and highly efficient reconstruction algorithm based on deep learning. In our approach, image reconstruction is performed with a deep convolutional neural network (CNN)

The parameters of many physical processes are unknown and have to be inferred from experimental data. The corresponding parameter estimation problem is often solved using iterative methods such as steepest descent methods combined with trust regions. For a few problem classes also continuous analogues of iterative methods are available. In this work, we expand the application of continuous analogues

We consider the problem of estimating the 2D vector displacement field in a heterogeneous elastic solid deforming under plane stress conditions. The problem is motivated by applications in quasistatic elastography. From precise and accurate measurements of one component of the 2D vector displacement field and very limited information of the second component, the method reconstructs the second component

In this paper we develop and validate with bootstrapping techniques a mechanistic mathematical model of immune response to both BK virus infection and a donor kidney based on known and hypothesized mechanisms in the literature. The model presented does not capture all the details of the immune response but possesses key features that describe a very complex immunological process. We then estimate model

We apply the adjoint weighted equation method (AWE) to the direct solution of inverse problems of incompressible plane strain elasticity. We show that based on untreated noisy displacements, the reconstruction of the shear modulus can be very poor. We link this poor performance to loss of coercivity of the weak form when treating problems with discontinuous coefficients. We demonstrate that by smoothing

We formulate an optimal design problem for the selection of best states to observe and optimal sampling times for parameter estimation or inverse problems involving complex nonlinear dynamical systems. An iterative algorithm for implementation of the resulting methodology is proposed. Its use and efficacy is illustrated on two applied problems of practical interest: (i) dynamic models of HIV progression

A numerical method for an inverse problem for an elliptic equation with the running source at multiple positions is presented. This algorithm does not rely on a good first guess for the solution. The so-called "approximate global convergence" property of this method is shown here. The performance of the algorithm is verified on real data for Diffusion Optical Tomography. Direct applications are in

Compton-scattering tomography is an imaging technique that exploits the energy dependence of Compton-scattered radiation. This image reconstruction problem is characterized by measurements of path integrals over circular arcs. In the conventional x-ray transmission computed tomography (CT) problem, the path integrals are along straight lines. We show that, with a simple transformation of variables

Based on Bayesian inference, an adaptive single component Metropolis–Hastings (SCMH) sampling algorithm is presented to estimate the surface heat flux which is a typical inverse heat conduction problem. The surface heat flux is expressed by two different basis functions, the piecewise linear function and the Fourier series, and for speeding up convergence process, the parameters of the Fourier series

Structural damage detection is a key part of structural health monitoring. The generalized flexibility matrix approach is an effective method for damage detection. Compared with the flexibility matrix approach, it requires less number of natural frequencies and corresponding mode shapes. In this paper, the approach is improved by considering the nonnegativity of the damage extent. The error bound of

The total variation (TV) minimization algorithms is a classical representative of the optimization algorithms and have been widely used for their simpleness, robustness, expandability and their potential of accurately reconstructing images from sparse data or noisy data. The commonly used constrained TV (cTV) program is the data-divergence constrained TV (DDcTV) minimization. The other recently proposed

In this paper, we consider the source strength identification problem for the three-dimensional inverse heat conduction equations. The problem is to determine an unknown heat source strength from the measurement data for a specified location. In this process, the direct problem is solved by applying the Green’s function method. Then, this problem can be converted into a Volterra integral equation of