Solution Of Inverse Problem Research Articles

A random walk based methodology to calculate the sensitivity coefficients in inverse radiant boundary design problems

Radiative heating furnaces are widely used for heat treatment applications in manufacturing industries. Strict requirements on heat treatment characteristics of the workpieces require precise control of furnace heater temperatures. Numerical techniques for the solution of inverse heat transfer problems can be used for the optimization of the radiant heater temperatures. In gradient-based optimization techniques, the optimization is carried out using the sensitivity coefficients between the heater and workpiece temperatures. In this study, we present a methodology for calculating the sensitivity coefficients for the solution of inverse boundary design problems involving transient heating of solid workpieces in a three-dimensional radiant furnace. In our methodology, the sensitivity coefficients on the selected design points within the workpieces are calculated by analytical differentiation of design point temperature formulations derived utilizing the floating random walk method and radiative heat flux formulation with exchange factors. The methodology for calculating sensitivity coefficients has been verified through applications to both a one-dimensional scenario and the three-dimensional radiant furnace model. The developed methodology was integrated into a gradient-based optimization algorithm in two test cases, to determine the furnace heater temperatures required to achieve the desired temperature histories at design points within the workpieces. First test case focuses reconstruction of an assumed heater temperature and examines the impact of design point configuration and input data noise on convergence behavior and calculated estimation. The findings reveal that increasing the number of design points in the workpieces increases solution accuracy, with transverse positioning of the design points in the workpieces resulting in heater temperatures closest to the assumed values. Second test case focused on estimating required heater temperatures for spatially uniform heating pattern on the workpieces. With 72 transversely positioned design points, we achieved uniform heating at these points with a maximum relative temperature deviation of 0.26%.

Electrical conductivity of the suboceanic upper mantle constrained by satellite-derived tidal magnetic fields: three-dimensional inversion, validation and interpretation

SUMMARY We present the first 3-D upper-mantle conductivity models obtained by an inversion of the satellite-derived tidally induced magnetic fields (TIMFs). We primarily use the M$_2$ period, but the potential benefit of the O$_1$ period is also inspected. The inverse-problem solution is found using the recently developed frequency-domain, spherical harmonic finite-element method based on the adjoint approach. We tested two different TIMF data sets derived from the satellite measurements of the Swarm mission and two different regularizations; the solution is either required to be sufficiently smooth or reasonably close to the a priori 3-D conductivity model WINTERC-e Wd-emax. The reconstructed conductivity models are locally compared with the 1-D conductivity profiles from other studies. If we use one of the available TIMF data sets, the smooth reconstructed model gravitates towards Wd-emax and the TIMF-adjusted Wd-emax model is closer to the reference conductivity profiles than the original Wd-emax model. Finally, we use the obtained 3-D conductivity distributions to calculate the corresponding 3-D water distribution in the upper mantle using thermodynamical and compositional models coupled to the electrical-conductivity laboratory measurement of individual mantle constituents.

Complex profile metrology via physical symmetry enhanced small angle x-ray scattering

Small angle x-ray scattering (SAXS) stands out as a promising solution in semiconductor metrology. The critical issue of SAXS metrology is to solve the SAXS inverse problem. With the increasing complexity of semiconductor devices, traditional strategies will face problems such as long iteration time and multiple solutions. To address these challenges, we develop a physical symmetry enhanced method to speed up the solution of the SAXS inverse problem for complex nanostructures. We incorporate the physical symmetry into a deep learning model, and a combined loss function is proposed to determine the correct structure in each step of training, which can continuously correct errors and make the model converge faster. The results show that the proposed method achieves high accuracy in determining the critical structural parameters of the complex profile gratings. Compared to traditional strategies, our method performs better in accuracy and does not require time-consuming iterations during reconstruction. The physical symmetry enhanced method provides a feasible way for achieving real-time reconstruction of complex profile nanostructures and is expected to promote the development of SAXS metrology.

Towards accuracy improvement in solution of inverse kinematic problem in redundant robot: A comparative analysis

AbstractThe redundant manipulators have more DOFs (degree of freedoms) than it requires to perform specified task. The inverse kinematic (IK) of such robots are complex and high nonlinear with multiple solutions and singularities. As such, modern Artificial Intelligence (AI) techniques have been used to address these problems. This study proposed two AI techniques based on Neural Network Genetic Algorithm (NNGA) and Particle Swarm Optimization (PSO) algorithm to solve the inverse kinematics (IK) problem of 3DOF redundant robot arm. Firstly, the forward kinematics for 3 DOF redundant manipulator has been established. Secondly, the proposed schemes based on NNGA and PSO algorithm have been presented and discussed for solving the inverse kinematics of the suggested robot. Thirdly, numerical simulations have been implemented to verify the effectiveness of the proposed methods. Three scenarios based on triangle, circular, and sine-wave trajectories have been used to evaluate the performances of the proposed techniques in terms of accuracy measure. A comparison study in performance has been conducted and the simulated results showed that the PSO algorithm gives 7% improvement compared to NNGA technique for triangle trajectory, while 2% improvement has been achieved by the PSO algorithm for circular and sine-wave trajectories.

Genetic Algorithm as the Solution of Non-Linear Inverse Heat Conduction Problems: A Novel Sequential Approach

Abstract Direct measurement of surface heat flux could be extremely challenging, if not impossible, in numerous applications. In such cases, the use of temperature measurement data from subsurface locations can facilitate the determination of surface heat flux and temperature through the solution of the inverse heat conduction problem (IHCP). Several different techniques have been developed over the years for solving IHCPs, with different levels of complexity and accuracy. The filter coefficient technique has proved to be a promising approach for solving IHCPs. Inspired by the filter coefficient approach, a novel method is presented in this paper for solving one-dimensional IHCPs in a domain with temperature-dependent material properties. A test case is developed in COMSOL Multiphysics where the front side of a slab is subject to known transient heat flux and the temperature distributions within the domain are calculated through numerical simulation. The IHCP solution in the form of filter coefficients is defined and a genetic algorithm (GA) is used for the calculation of filter matrix. The number of significant filter coefficients required to evaluate surface heat flux at each time-step is determined through trial and error and the optimal number is selected for evaluating the solution. The structure of the filter matrix is assessed and discussed. The resulting filter coefficients are then used to evaluate the surface heat flux for several different test cases and the performance of the proposed approach is assessed in detail. The results showed that the presented approach is robust and can result in finding optimal filter coefficients that can accurately estimate various types of surface heat flux profiles using temperature data from a limited number of time steps and in a near real-time fashion.

Nonintrusive thermal contact conductance estimation in double-layered pipelines: A reciprocity functional method perspective

Thermal contact conductance (TCC) is a critical factor in various engineering applications involving heat transfer between solid surfaces. Accurate knowledge of TCC enables a more precise thermal system analysis, leading to improved efficiency, reduced energy consumption, and prevention of thermal damages. Moreover, TCC estimation can help to identify material discontinuities or failures. A recent tool for TCC estimation is the Reciprocity Functional Method (RFM) coupled with the Classical Integral Transform Technique (CITT). This method allows the solution of inverse boundary value problems without the need of iterative methods or intrusive measurements, making it valuable for nondestructive testing of interfacial flaws between solid materials. Furthermore, it enables the computation of TCCs using analytical expressions, resulting in a computationally fast procedure. The technique involves the solution of two auxiliary problems: one for the temperature discontinuity estimation, and the other for the interfacial heat flux estimation, both at the inaccessible interface between the two contacting materials. In this study, we applied the RFM and the CITT to estimate different types of TCCs, using a three-dimensional double-layer hollow cylinder geometry as a representative model, like double-layer pipelines used in the oil industry. Temperature measurements for solving the inverse problem were considered available on the outer surface of the pipe which, in the case of a real experiment, could be obtained via an infrared camera. The results demonstrated a good estimate for various analyzed test-cases, even when the measurements were contaminated with Gaussian noises.

Алгоритм визначення параметрів включення при розв’язуванні обернених задач геоелектророзвідки методом про

The paper aims to develop an algorithm for recognizing the physical and geometric parameters of inclusion, using indirect methods of boundary, near-boundary, and partially-boundary elements based on the data of the potential field. Methodology. The direct and inverse two-dimensional problems of the potential theory concerning geophysics were solved when modeling the earth's crust with a piecewise-homogeneous half-plane composed of a containing medium and inclusion that are an ideal contact. To construct the integral representation of the solution of the direct problem, a special fundamental solution for the half-plane (Green's function) of Laplace's equation, which automatically satisfies the zero-boundary condition of the second kind on the day surface, and a fundamental solution for inclusion were used. To find the intensities of unknown sources introduced in boundary, near-boundary, or partially-boundary elements, the collocation technique was used, i.e. the conditions of ideal contact are satisfied in the middle of each boundary element. After solving the obtained SLAE, the unknown potential in the medium and inclusion and the flow through their boundaries are found, considering that the medium and inclusion are considered as completely independent domains. Results. The computational experiment for the task of electric prospecting with a constant artificial field using the resistance method, in particular, electrical profiling, was carried out, while focusing on the physical and geometric interpretation of the data. Initial approximations for the electrical conductivity of the inclusion, its center of mass, orientation and dimensions are determined by the nature of the change in apparent resistivity. To solve the inverse problem two cascades of iterations are organized: the first one is to specify the location of the local heterogeneity and its approximate dimensions, the second one is to specify its shape and orientation in space. At the same time, the minimization of the functional considered on the section of the boundary, where an excess of boundary conditions is set, is carried out. Originality. The method of boundary integral equations is shown to be effective for constructing numerical solutions of direct and inverse problems of potential theory in a piecewise homogeneous half-plane, using indirect methods of boundary, near-boundary, and partial-boundary elements as variants. Practical significance. The proposed approach for solving the inverse problem of electrical exploration with direct current is effective because it allows fora step-by-step, "cascade" recognition of the shape, size, orientation, and electrical conductivity of the inclusion. We follow the principle of not using all the details of the model and not attempting to recognize parameters with little effect on the result, especially with imprecise initial approximations.

Solution of Inverse Geometric Problems Using a Non-Iterative MFS

Solution of Inverse Geometric Problems Using a Non-Iterative MFS

Deep Learning Electromagnetic Inversion Solver Based on a Two-Step Framework for High-Contrast and Heterogeneous Scatterers

Deep Learning Electromagnetic Inversion Solver Based on a Two-Step Framework for High-Contrast and Heterogeneous Scatterers

A neural network inverse problem solution for a MIMO magnetic levitation actuator

A multiple-input and multiple-output planar actuator is proposed, which utilizes mechanically driven stator magnet arrays to levitate a permanent magnet mover. A state of levitation and actuation is obtained by mechanically altering the orientation of the stator magnets to control the forces and torques on the mover. A challenge for the design and control of the actuator is inverting the relationship between the force and stator magnet rotation angles, as there is no closed-form analytical solution. In this study, a feed-forward neural network is applied to model the forward relation between stator magnet angle input and a force and torque output to reduce the forward computation time for the design process and for error estimation in real-time applications. Additionally, the neural network is considered for inverting the solution for a motion profile sampled at 1000 Hz. The developed forward model is able to calculate the forces and torques on the mover a factor 10 faster than the equivalent charge or Fourier model with an absolute error of 3 mN and 0.1 mNm for the forces and torques, respectively, and a feed-forward neural network is able to accurately learn an inverse solution for small motion profiles.

Evaluation of the influence of an aggressive environment on the durability of the cement stone

The paper proposes methods for assessing the durability of building materials and structures based on Portland cement when exposed to aggressive environments that mimic the products of the vital activity of bacteria on building materials. To determine the main parameters of the model of degradation of building materials under the action of aggressive environments, a mathematical model has been developed in the form of integral and differential relations connecting these parameters. A technique for identifying the mechanical characteristics included in these models based on the solution of inverse biodegradation problems has been developed. The analysis of changes in the structure of the cement stone was carried out using the results of computed tomography, and the regularities of the distribution of pores in the cement stone from the time of exposure were obtained. Based on experimental and numerical studies, it has been established that the mechanism of destruction of cement stone obtained by the traditional method and activation in the vortex layer apparatus is different. The difference lies in the greater accumulation of cement stone interaction products in the activated sample, which is confirmed by a shift in porosity to less than 0.5 mm and a lower solubility value compared to the control composition. The compressive strength of the samples as a result of exposure for 28 days decreased by 37% and 20% for the control and activated compositions. The mass of the studied samples as a result of exposure decreased by 49% and 21%, respectively. On the basis of this mechanism, a mathematical model of the process of material degradation in an aggressive one is developed, taking into account changes in porosity and acidity concentration, and dependence of material strength reduction are obtained.

Inverse Problem of Determining the Unknown Coefficients in an Elliptic Equation

The inverse problem of determining the coefficients of an elliptic equation under different boundary conditions in a given rectangle is considered. These problems lead to the necessity of approximate solution of inverse problems of mathematical physics, which are incorrect in the classical sense. The existence, uniqueness, and stability theorems for the solution of the set inverse problem are proved and a regularizing algorithm for determining the coefficient is constructed.

Determining relative permeability and capillary pressure from mixed-wet core floods

The main goal of this paper is a laboratory method development for determining the capillary pressure and relative permeability from coreflooding test specifically for mixed-wet rocks. Previously, the steady-state transient test (SSTT) was designed to determine both relative permeability (Kr) and capillary pressure (Pc) from a single steady-state coreflood by using the transient data of routine steady-state tests. On the contrary to the previous works, where SSTT was developed for completely hydrophobic or hydrophilic outcrop cores, this paper determines Kr and Pc for mixed-wet cores. Depending on the capillary pressure equation applied, the mathematical model for two-phase flow in mixed-wet rocks contains one or two extra constants, so some extra measurements must be taken during SSTT, to determine Pc and Kr curves. We change the experimental protocol by establishing a uniform initial saturation Swi by evaporation method. We also include bump floods at two high rates for the alternative determination of saturation and relative permeability for residual oil. A new inverse solver determines the set of model constants that employs van Genuchten's Pc formula and a vaporization procedure for initial core saturation. The number of resulting model coefficients is equal to seven and matches the dimension of the measured data array for mixed-wet cores.The developed SSTT for mixed-wet rocks is applied and validated for both high-salinity (HS) and low-salinity (LS) waterfloods. Strong agreement between laboratory steady-state, transient, and bump-flood data and those obtained by mathematical modelling – R2 is above 0.99 for steady-state data and above 0.9 for transient data - validates the proposed SSTT procedure and inverse solver for mixed-wet cores and HS and LS waterfloods. Our findings indicate that low salinity has a greater effect in expanding the range of positive capillary pressure compared to high salinity. This suggests an increase in water-wettability as the salinity decreases.

Effects of phantom microstructure on their optical properties.

Developing stable, robust, and affordable tissue-mimicking phantoms is a prerequisite for any new clinical application within biomedical optics. To this end, a thorough understanding of the phantom structure and optical properties is paramount. We characterized the structural and optical properties of PlatSil SiliGlass phantoms using experimental and numerical approaches to examine the effects of phantom microstructure on their overall optical properties. We employed scanning electron microscope (SEM), hyperspectral imaging (HSI), and spectroscopy in combination with Mie theory modeling and inverse Monte Carlo to investigate the relationship between phantom constituent and overall phantom optical properties. SEM revealed that microspheres had a broad range of sizes with average and were also aggregated, which may affect overall optical properties and warrants careful preparation to minimize these effects. Spectroscopy was used to measure pigment and SiliGlass absorption coefficient in the VIS-NIR range. Size distribution was used to calculate scattering coefficients and observe the impact of phantom microstructure on scattering properties. The results were surmised in an inverse problem solution that enabled absolute determination of component volume fractions that agree with values obtained during preparation and explained experimentally observed spectral features. HSI microscopy revealed pronounced single-scattering effects that agree with single-scattering events. We show that knowledge of phantom microstructure enables absolute measurements of phantom constitution without prior calibration. Further, we show a connection across different length scales where knowledge of precise phantom component constitution can help understand macroscopically observable optical properties.

Solving forward and inverse problems of contact mechanics using physics-informed neural networks

This paper explores the ability of physics-informed neural networks (PINNs) to solve forward and inverse problems of contact mechanics for small deformation elasticity. We deploy PINNs in a mixed-variable formulation enhanced by output transformation to enforce Dirichlet and Neumann boundary conditions as hard constraints. Inequality constraints of contact problems, namely Karush–Kuhn–Tucker (KKT) type conditions, are enforced as soft constraints by incorporating them into the loss function during network training. To formulate the loss function contribution of KKT constraints, existing approaches applied to elastoplasticity problems are investigated and we explore a nonlinear complementarity problem (NCP) function, namely Fischer–Burmeister, which possesses advantageous characteristics in terms of optimization. Based on the Hertzian contact problem, we show that PINNs can serve as pure partial differential equation (PDE) solver, as data-enhanced forward model, as inverse solver for parameter identification, and as fast-to-evaluate surrogate model. Furthermore, we demonstrate the importance of choosing proper hyperparameters, e.g. loss weights, and a combination of Adam and L-BFGS-B optimizers aiming for better results in terms of accuracy and training time.

A once-through artificial neural network approach for used nuclear fuel inverse depletion analysis: A comparative study

This work addresses the challenge of identifying the origins and burnup history of used nuclear fuel, which is crucial for safeguarding and non-proliferation analysis. It presents a comparative evaluation of two distinct computational approaches to bundles at the same in-core position: the first entails building a forward Artificial Neural Networks (ANN) surrogate model for fuel inventory prediction followed by solving the inverse depletion problem using an optimization solver. The second approach is to build an inverse ANN model that relates the used nuclear fuel inventory to its initial and burnup conditions (a once-through approach), eliminating the need for the inverse optimization solver step which results in better accuracy, less computational costs, and renders the application of such approach practical. KENO VI depletion model is utilized to deplete a VVER assembly model generating the necessary datasets for the ANN inverse model training and validation. The inverse model is then employed to estimate the initial composition and the burnup for several test cases. The results are then compared to the known initial and burnup conditions as well as to the estimations made by benchmark results from an existing ANN forward surrogate model combined with the Particle Swarm Optimization (PSO) solver. Comparative analyses across eight scenarios consistently reveal that the once-through ANN inverse model has superior accuracy and consistency in terms of estimating the actual burnup and initial fuel enrichment with a relative root mean squared error (RMSE) of 1.20×10-2 compared to the benchmark approach (ANN-PSO) which yielded a relative RMSE of 2.18×10-2. Moreover, the once-through inverse approach has a significantly lower computational cost as it requires 1 inverse model run compared to the 9,450,000 model runs required by the benchmark approach (ANN-PSO). Overall, the results demonstrate that the proposed once-through approach simplifies and enhances the efficiency of solving the inverse fuel depletion problem while outperforming the benchmark approach in terms of predictive accuracy computational cost.

Estimation of Oil Reservoir Transmissivity and Storativity Fields Using a Radial Basis Function Network Based on Inverse Problem Solving

Estimation of Oil Reservoir Transmissivity and Storativity Fields Using a Radial Basis Function Network Based on Inverse Problem Solving

Informed Adaptive Sensing.

For many inverse problems, the data on which the solution is based is acquired sequentially. We present an approach to the solution of such inverse problems where a sensor can be directed (or otherwise reconfigured on the fly) to acquire a particular measurement. An example problem is magnetic resonance image reconstruction. We use an estimate of mutual information derived from an empirical conditional distribution provided by a generative model to guide our measurement acquisition given measurements acquired so far. The conditionally generated data is a set of samples which are representative of the plausible solutions that satisfy the acquired measurements. We present experiments on toy and real world data sets. We focus on image data but we demonstrate that the method is applicable to a broader class of problems. We also show how a learned model such as a deep neural network can be leveraged to allow generalisation to unseen data. Our informed adaptive sensing method outperforms random sampling, variance based sampling, sparsity based methods, and compressed sensing.

Determination of transient heat transfer by cooling channel in high-pressure die casting using inverse method

Complex shapes of aluminum castings are typically manufactured during the short cycle process known as the high-pressure die casting (HPDC). High productivity is ensured by introducing die cooling through a system of channels, die inserts or jet coolers. Die cooling can also effectively help in reducing internal porosity in cast components. Accurate simulations based on sophisticated numerical models require accurate input data such as material properties, initial and boundary conditions. Although the heat is dominantly dissipated through die cooling, indicating the importance of knowing precise thermal boundary conditions, open literature lacks a detailed information about the spatial distribution of heat transfer coefficient. This study presents an inverse method to determine accurate heat transfer coefficients of a die insert based on temperature measurements in multiple points by 0.5 mm K-type thermocouples and a subsequent solution of the two-dimensional inverse heat conduction problem. The solver was built in the open-source CFD code OpenFOAM and the free library for nonlinear optimization NLopt. The results are presented for the commonly used 10 mm die insert with a hemispherical tip and coolant flow rates ranging from 100 l/h to 200 l/h. Heat transfer coefficients reach values well above 50 kW/m2K in the hemispherical tip, which is followed by a secondary peak and then a gradual drop to values around 1 kW/m2K further downstream.

An inversion problem for optical spectrum data via physics-guided machine learning

We propose the regularized recurrent inference machine (rRIM), a novel machine-learning approach to solve the challenging problem of deriving the pairing glue function from measured optical spectra. The rRIM incorporates physical principles into both training and inference and affords noise robustness, flexibility with out-of-distribution data, and reduced data requirements. It effectively obtains reliable pairing glue functions from experimental optical spectra and yields promising solutions for similar inverse problems of the Fredholm integral equation of the first kind.