Iterative Inversion Method Research Articles

Ultrasound-based Eigenfrequency Analysis to Determine Material Parameters of Tissue Mimicking Phantoms

Abstract A modern area of research in cancer treatment is magnetic drug targeting (MDT) with superparamagnetic iron oxide nanoparticles (SPIONs). In order to understand the processes involved in MDT in more detail and to be able to perform this therapy as efficiently as possible, a monitoring system for the spatial distribution of SPIONs in biological tissue is required. One approach is to use magnetomotive ultrasound (MMUS) to monitor the spatial distribution over time. However, the spatial distribution of SPIONs cannot be quantitatively determined applying basic MMUS algorithms. Therefore, MMUS has been extended by a simulation part to quantitatively determine the spatial distribution of SPIONs. This extended MMUS algorithm requires the material parameters and the geometry of the target tumorous tissue. In this contribution, we describe an ultrasound-based eigenfrequency analysis combined with an iterative inverse simulation-based method to determine the mechanical parameter Young's modulus of tissue mimicking phantoms. The presented approach yields a good estimate of the Young's modulus compared to the result from a compression test.

Geostatistical Inversion of Frequency-Domain Electromagnetic Data for Near Surface Modelling

The detailed characterization of near-surface deposits is important for both environmental and economic reasons. These shallow subsurface systems can be very complex and heterogenous due to natural dynamics and anthropogenic interferences. Modeling techniques based exclusively on direct sampling generate limited informed three-dimensional models of the near-surface. Geophysical methods provide valuable and additional information to model the spatial distribution of the near-surface for locations where direct observations are not available. From this set of methods, frequency-domain electromagnetic induction (FDEM) has been successfully applied to image complex near-surface deposits. Yet, predicting the spatial distribution of relevant subsurface properties from geophysical data, and the integration of direct observations, is not straightforward. It requires solving a challenging geophysical inversion problem. Geostatistical modelling tools have been effectively applied to couple direct observations with geophysical data such as seismic reflection. We propose an iterative geostatistical FDEM inversion method able to integrate data from direct measurements of the near-surface with surface loop-loop FDEM measurements to simultaneously predict high-resolution models of electrical conductivity and magnetic susceptibility, and their associated uncertainty. The iterative geostatistical inversion method is based on stochastic sequential simulation and co-simulation as model perturbation and update techniques. The iterative optimization is based on the local data misfit between observed and simulated FDEM data, weighted by the sensitivity of the acquisition equipment. The proposed method is first demonstrated for a synthetic landfill data set created based on real data collected at a mine tailing disposal site in Portugal, and on a real data set collected at a site with archaeological features in Knowlton, UK. The results show the ability of the proposed method to accurately predict and characterize the spatial distribution of electrical conductivity and magnetic susceptibility down to the depth of interest while reproducing the recorded FDEM data.

Defect characterization from magnetic field leakage signals in petroleum and natural gas pipelines

Pipelines transport invaluable energy resources such as crude oil and natural gas over long distances. The integrity of the piping system in terms of safety of the process is then of high importance. However, pipes are prone by time to defects that may degrade their properties and lead to failures. In this paper, we study the effect of defect parameters on the magnetic field leakage captured by Hall sensors operating along the pipe. In fact, the obtained results show that the defect parameters influence directly the MFL amplitude and shape. For this reason, the inversion problem allowing us to reconstruct the defect from the MFL signals became fast and easier in comparison to the deterministic and probabilistic algorithm inversion procedure. However, the simplified system cannot describe the real defects and the three-dimensional numerical study became necessary. In tank floor inspection domain, as our recent published work, we have studied the performance of defect shape reconstruction from MFL array sensor imaging and depth estimation while using an iterative inversion method. Indeed, the first stage consists of determining the defect width and length from magnetic flux leakage mapping reconstructed from the recorded signals of the micro-integrated magnetic sensors. Then, after coupling Comsol and Matlab software, the defect depth is obtained by coupling the 3D finite elements method and a fast iterative algorithm recently developed. Consequently, the defect shape and size are obtained after a few iterations with high precision. Furthermore, this method of defect reconstruction and seizing can be extended for irregular defect shapes encountered in pipeline such as cracks and corrosion.

Identification of hardening and fracture behaviors of titanium alloy by a hybrid digital image correlation and finite element method

The reliable identification of deformation and fracture behaviors of titanium alloys is essential for accurate numerical simulation in sheet metal forming, cutting process and crash. In this study, an inverse method is proposed to identify both strain hardening and fracture behavior of titanium alloys by a hybrid experimental-finite element analysis. Uniaxial and notched tensile specimens are tested on the additively manufactured and cold rolled sheet Ti6Al4V alloys. The distributions of displacement and strain on the specimen surface during the loading are measured by digital image correlation method. An identification strategy, considering the stress–strain curve, surface strain evolution and variation of specimen width, is proposed to identify the strain hardening model parameters at large strain range. Finite element simulations are performed to update the model parameters by using the iterative inverse method. The parameters of fracture model are determined through experiments on tensile specimens in combination with numerical simulation. The experimental and simulation results show the feasibility and effectiveness of the proposed identification method, that it can be further used to characterize the plastic and fracture behaviors of other metallic materials in practice.

Numerical Investigation of the Quantum Inverse Algorithm on Small Molecules.

We evaluate the accuracy of the quantum inverse (Q-Inv) algorithm, in which the multiplication of Ĥ-k to the reference wave function is replaced by the Fourier transformed multiplication of e-iλĤ, as a function of the integration parameters and the iteration power k for various systems, including H2, LiH, BeH2 and the notorious H4 molecule at square geometry. We further consider the possibility of employing the Gaussian-quadrature rule as an alternate integration method and compared it to the results employing trapezoidal integration. The Q-Inv algorithm is compared to the inverse iteration method using the Ĥ-1 inverse (I-Iter) and the exact inverse by lower-upper decomposition. Energy values are evaluated as the expectation values of the Hamiltonian. Results suggest that the Q-Inv method provides lower energy results than the I-Iter method up to a certain k, after which the energy increases due to errors in the numerical integration that are dependent on the integration interval. A combined Gaussian-quadrature and trapezoidal integration method proved to be more effective at reaching convergence while decreasing the number of operations. For systems like H4, in which the Q-Inv cannot reach the expected error threshold, we propose a combination of Q-Inv and I-Iter methods to further decrease the error with k at lower computational cost. Finally, we summarize the recommended procedure when treating unknown systems.

Solving inverse problems in magnetic field leakage sensor array inspection of petroleum tank floor

The MFL method is a qualitative inspection tool and is a reliable, fast, and economical nondestructive testing method for tank floors. In this paper, before presenting the defect reconstruction procedure, we studied the effect of defect parameters on the magnetic field leakage measured by a single Hall sensor. As predicted, the study of each parameter has demonstrated that any variation in the geometrical parameters of the studied defect induce a significant influence on the MFL signal amplitude and distribution; for this reason, all the defect parameters must be determined precisely and prudently. After that, we have studied the performance of defect shape reconstruction from MFL array sensor imaging and depth estimation while using an iterative inversion method. Indeed, the first stage consists of determining the defect width and length from magnetic flux leakage mapping reconstructed from the recorded signals of the micro-integrated magnetic sensors. As a second step, after coupling Comsol and Matlab software, the defect depth is obtained by coupling the 3D finite elements method and a fast iterative algorithm recently developed. Consequently, the defect shape and size are obtained after a few iterations with a relative error of less than 2%; which makes this method very appropriate for real-time defect reconstruction and quantification. Furthermore, this method of defect reconstruction and seizing can be extended for irregular shape such as cracks and corrosion. In fact, this can be done while subdividing the affected area of non-constant depth into elementary zones of a constant depths. Then, while modifying the previous algorithm, we determine the corresponding depth of each zone.

Derived Coarse-Grained Potentials for Semicrystalline Polymers with a Blended Multistate Iterative Boltzmann Inversion Method.

In this article, we employ the multistate iterative Boltzmann inversion (MS-IBI) method to develop coarse-grained potentials capable of representing molecular structure in both the amorphous and crystalline phases of semicrystalline polymers with improved accuracy while allowing for tunable control over the dynamics governing the α-relaxation process. A unique feature of this method is that the potentials are blended using the product of the target structural distributions, for example, the radial density function, for each phase and a weighting factor. To demonstrate this approach, a family of potentials for polyethylene is developed where the weighting factor of the crystalline phase ranges is varied from zero, incorporating information only from the amorphous phase, to unity, where the model is trained from only the crystalline phase. The most accurate representation of structural distributions was obtained when the crystalline phases is weighted at 50%. However, we show that when the crystalline phase is weighted at 90%, the model more accurately represents dynamics of the α-relaxation process, with realistic predicted values of activation energy and diffusion rates, with relatively minor impact on accuracy in structure.

A robust numerical strategy for finding surface waves in flows of non-Newtonian liquids

Gravity-driven flows of liquid films are frequent in nature and industry, such as in landslides, lava flow, cooling of nuclear reactors, and coating processes. In many of these cases, the liquid is non-Newtonian and has particular characteristics. In this paper, we analyze numerically the temporal stability of films of non-Newtonian liquids falling by gravity, on the onset of instability. The liquid flows over an incline, where surface waves appear under certain conditions, and we do not fix a priori its rheological behavior. For that, we made used of the Carreau–Yasuda model without assigning specific values to its constants, and we compute general stability solutions. The numerical strategy is based on expansions of Chebyshev polynomials for discretizing the Orr–Sommerfeld equation and boundary conditions, and a Galerkin method for solving the generalized eigenvalue problem. In addition, an Inverse Iteration method was implemented to increase accuracy and improve computational time. The result is a robust and light numerical tool capable of finding the critical conditions for different types of fluids, which we use to analyze some key fluids. We show that the outputs of the general code match previous solutions obtained for specific computations. Besides increasing our knowledge on surface-wave instabilities in non-Newtonian liquids, our findings provide a new tool for obtaining comprehensive solutions on the onset of instability.

Study of the Thermal-Hydraulic Characteristics of a Printed Circuit Heat Exchanger Using a Novel Iterative Inversion Method Combined with Genetic Algorithm

Printed circuit heat exchangers are getting more and more applications in various energy systems. Detailed data monitoring is essential to understand their operation situations in real time. Nevertheless, the commonly monitored parameters are inadequate to evaluate the local flow and heat transfer characteristics when the fluid undergoes an obvious property variation in the channel. In this work, a measurement system for printed circuit heat exchangers similar to those in industrial applications was set up to study the thermal-hydraulic characteristics of supercritical CO2 with non-linear physical properties. The experimental results show that the heat transfer coefficient can be increased by 82.9–109.6% when the mass flow rate increases from 0.15 to 0.42 kg/s. By comparison, the heat transfer coefficient can be increased by 70.7% when the fluid state approaches the critical point. A novel iterative inversion method was proposed to deduce the coefficients of the heat transfer and friction factor correlations based on the collected fundamental parameters. The deviations of the heat transfer rate and friction coefficient between the measured data and the predicted results by the derived correlations were both within 10%, indicating the feasibility and reliability of the inversion method.

Inversion géostatistique par itérations de la tomographie de résistivité électrique

AbstractElectrical resistivity tomography (ERT) is a geophysical method used to create an image of the subsurface due to its sensitivity to porosity, water saturation, and pore fluid salinity. This geophysical method has been widely applied in the investigation of mineral and groundwater resources, as well as in archaeological, environmental, and engineering studies. The prediction of subsurface properties, such as electrical conductivity, from measured ERT data requires solving a challenging geophysical inversion problem. This work proposes an iterative geostatistical resistivity inversion method using stochastic sequential simulation and co-simulation as stochastic model perturbation and update techniques. Electrical resistivity models are generated conditioned to a target histogram, often retrieved from available resistivity borehole data, and assuming a spatial continuity pattern described by a variogram model. From the electrical resistivity models, a finite-volume approximation of Poisson’s equation is used to compute synthetic ERT data. The misfit between predicted and observed data drives the convergence of an iterative procedure and conditions the co-simulation of new models in the subsequent iterations. This methodology is applied to a two-dimensional synthetic case, and a set of two-dimensional profiles obtained from an ERT survey carried out in southern Portugal. In both application examples, the final models predict ERT data that match the observed ones while reproducing borehole data and imposed variogram models. The results obtained in both data sets are compared against a commercial deterministic ERT inversion methodology, showing the ability of the proposed method to model small-scale variability and assess spatial uncertainty.

2D magnetotelluric inversion based on ResNet

In this study, a deep learning algorithm was applied to two-dimensional magnetotelluric (MT) data inversion. Compared with the traditional linear iterative inversion methods, the MT inversion method based on convolutional neural networks (CNN) does not rely on the selection of the initial model parameters and does not fall into the local optima. Although the CNN inversion models can provide a clear electrical interface division, their inversion results may remain prone to abrupt electrical interfaces as opposed to the actual underground electrical situation. To solve this issue, a neural network with a residual network architecture (ResNet-50) was constructed in this study. With the apparent resistivity and phase pseudo-section data as the inputs and with the resistivity parameters of the geoelectric model as the training labels, the modified ResNet-50 model was trained end-to-end for producing samples according to the corresponding production strategy of the study area. Through experiments, the training of the ResNet-50 with the dice loss function effectively solved the issue of over-segmentation of the electrical interface by the cross-entropy function, avoided its abrupt inversion, and overcame the computational inefficiency of the traditional iterative methods. The proposed algorithm was validated against MT data measured from a geothermal field prospect in Huanggang, Hubei Province, which showed that the deep learning method has opened up broad prospects in the field of MT data inversion.

Machine learning-accelerated aerodynamic inverse design

The computational cost of iterative design methods has been a challenge in aerodynamics. In this research, the data-driven acceleration of an iterative inverse design method was implemented to reduce its computational cost. Although iterative design methods are robust, a lot of unwanted data is generated during their intermediate stages. Inverse design methods rely on correcting an initial geometry based on a given target parameter distribution. The generated data during the early iterations of the inverse design was incorporated into two deep-learning models to accelerate target geometry attainment. The deep learning models were used to recognize the correlation between the pressure distribution and corresponding geometry as well as the meaningful changes of geometry and pressure distribution toward their targets. The deep learning models were validated in viscous and inviscid compressible flows for various benchmark aerodynamics problems. In conclusion, between 70 to 80% computational cost decrease was observed for online uses of the machine learning module with the inverse design algorithm. This approach suggests incorporating machine learning techniques into design algorithms by exploiting the intermediate data for further improvement of them. We draw a new interpretation of learning dynamic changes through consecutive iterations instead of typical time-dependent problems in the use of LSTM network.

Iterative approaches for regional Moho determination using on-orbit gravity gradients: A case study in Qinghai-Tibet Plateau and its near zone

Summary Moho determination is an important issue in studying the Earth’s interior structure. In accordance with the isostasy-compensation hypothesis in geodesy, it is possible to recover regional or global Moho by employing gravimetric data. The non-linear property is one of the main difficulties in solving the inverse problem of isostasy. To effectively address this issue, we propose an improved iterative inversion method that combines three-dimensional integration and linear regularization to achieve an approximate non-linear solution. To estimate the contributions of different components in the gravity-gradient tensor from the Gravity field and steady-state Ocean Circulation Explorer (GOCE), other than the vertical component, we additionally develop two joint inversion scenarios that utilize diagonal horizontal components and all five non-vertical components. The validating experiments are implemented in Qinghai-Tibet Plateau and its near zone. Simulations and applications illustrate that horizontal responses of Moho undulation are also significant. Yet the off-diagonal components provide minimal contributions, adding only 0.25 km of bias to the joint inversion results. Truncation effects serve as the primary source of systematic errors, resulting in ∼1 km error in vertical inversion results and ∼2.3 km error in joint inversion results. Then, the gravimetric Moho results are compared with CRUST1.0, and they show a generally strong correlation. Differences are obvious at the northern and eastern margins of the plateau. It is maybe due to the local changes in crust-mantle density contrasts. Upwelling of asthenospheric materials and fluid flow in the middle-lower crust are the two main factors. Based on high-precision satellite gravimetry, our study could provide new insights into the tectonic structure of Qinghai-Tibet Plateau.

Enhanced full-inversion-based ultrasound elastography for evaluating tumor response to neoadjuvant chemotherapy in patients with locally advanced breast cancer

PurposeAn enhanced ultrasound elastography technique is proposed for early assessment of locally advanced breast cancer (LABC) response to neoadjuvant chemotherapy (NAC). MethodsThe proposed elastography technique inputs ultrasound radiofrequency data obtained through tissue quasi-static stimulation and adapts a strain refinement algorithm formulated based on fundamental principles of continuum mechanics, coupled with an iterative inverse finite element method to reconstruct the breast Young’s modulus (E) images. The technique was explored for therapy response assessment using data acquired from 25 LABC patients before and at weeks 1, 2, and 4 after the NAC initiation (100 scans). The E ratio of tumor to the surrounding tissue was calculated at different scans and compared to the baseline for each patient. Patients’ response to NAC was determined many months later using standard clinical and histopathological criteria. ResultsReconstructed E ratio changes obtained as early as one week after the NAC onset demonstrate very good separation between the two cohorts of responders and non-responders to NAC. Statistically significant differences were observed in the E ratio changes between the two patient cohorts at weeks 1 to 4 after treatment (p-value < 0.001; statistical power greater than 97%). A significant difference in axial strain ratio changes was observed only at week 4 (p-value = 0.01; statistical power = 76%). No significant difference was observed in tumor size changes at weeks 1, 2 or 4. ConclusionThe proposed elastography technique demonstrates a high potential for chemotherapy response monitoring in LABC patients and superior performance compared to strain imaging.

Learning-Assisted Inversion for Solving Nonlinear Inverse Scattering Problem

Solving inverse scattering problems (ISPs) is challenging because of its intrinsic ill-posedness and the nonlinearity. When dealing with highly nonlinear ISPs, i.e., those scatterers with high contrast and/or electrically large size, the traditional iterative nonlinear inversion methods converge slowly and take lots of computation time, even maybe trapped into local wrong solution. To alleviate the above challenges, a learning-assisted (LA) inversion approach termed as the LA inversion method (LAIM) with advanced generative adversarial network (GAN) in virtue of a new recently established contraction integral equation for inversion (CIE-I) is proposed to achieve a good balance between the computational efficiency and the accuracy of solving highly nonlinear ISPs. The preliminary profiles composed of only small amount of low-frequency components can be got efficiently by the Fourier bases expansion of CIE-I inversion (FBE-CIE-I). The physically exacted information can be taken as the input of the neural network to recover super-resolution image with more high-frequency components. A weighted loss function composed of the adversarial loss, mean absolute percentage error (MAPE), and structural similarity (SSIM) is used under the pix2pix GAN framework. In addition, the self-attention module is used at the end of the generator network to capture the physical distance information between two pixels and enhance the inversion accuracy of the feature scatterers. To further improve the inversion efficiency, the data-driven method (DDM) is used to achieve real-time imaging by cascading U-net and pix2pix GAN, where U-net is used to replace FBE-CIE-I in the LAIM. Compared with other LA inversion, both the synthetic and experimental examples have validated the merits of the proposed LAIM and DDM.

Estimating model parameters from SP anomaly of sheet-shaped sources using differential search and particle swarm optimization algorithms

Abstract In this study, the efficiency of estimating the model parameters of sheet-shaped single and multiple sources of the self-potential (SP) anomaly using the differential search algorithm (DSA) is investigated. First, noise-free and noisy synthetic anomalies are calculated for a single sheet-shaped source, and its model parameters estimated by DSA. The DSA inversion is also done for a model consisting of three inclined sheets. To test the effectiveness of the method, the same processes are repeated with a more conventional algorithm, particle swarm optimization (PSO), and the solutions of both methods are compared. The results of synthetic anomaly analyses show that DSA can predict the parameters as accurately as PSO. Then, both algorithms are also applied to two field SP anomalies (Surda and Beldih) that have been evaluated by different algorithms in the literature. The source of the Surda anomaly is modelled as one sheet, whereas the source model of the Beldih anomaly is assumed to consist of three sheets. The five model parameters for each model are estimated using both algorithms and it is determined that they are in good agreement with the findings of the previous studies. The contribution of the regional background anomaly to the synthetic and field anomalies are also included and regional coefficients are estimated. Finally, we conclude that DSA can solve the source parameters without the need for the initial values required in conventional iterative inversion methods and is an efficient and promising algorithm for determining the parameters of SP sources.

Temperature Transferable and Thermodynamically Consistent Coarse-Grained Model for Binary Polymer Systems

For the simulations of polymer systems, coarse-grained (CG) models are often developed to tackle the length and time scale limitations that are not feasible by all-atom molecular dynamic simulations. However, due to the necessary simplification or reduction in atomistic degrees of freedom, CG models usually have poor transferability over various temperatures, compositions, or thermodynamic states. In this work, the structure-based iterative Boltzmann inversion (IBI) method is further developed to obtain temperature transferable and thermodynamically consistent CG potentials for binary polymer systems. In particular, the conventional IBI procedure is first utilized to optimize single-component CG potentials from homopolymer systems while cross-interaction potentials from a random block copolymer system. Afterward, a thermodynamic integration method is applied to refine the cross-interaction potential between two constituent components in binary systems until the Flory–Huggins parameter (χ) between two components is matched with experimental value. We apply the above optimization procedure for the polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) as an example, which is widely studied experimentally, and the χ value can be easily obtained in the literature. To validate the transferability of the obtained CG potential, systems of both PS and PMMA homopolymers, random block copolymers, diblock copolymers, and PS/PMMA blends with various compositions are simulated. Many properties, including the mass density, radius distribution function, and bonded distribution functions, between CG beads generated from CG simulations match very well with those from atomistic simulations in the simulated temperature range, i.e., from 453 to 500 K. More importantly, phase morphologies of diblock copolymers and phase diagram of PS/PMMA binary blends over wide temperature and compositional ranges generated from CG simulations using our model are in good agreement with experimental results and predictions from self-consistent field theory.

A Fast Algorithm of Cross-Correlated Contrast Source Inversion in Homogeneous Background Media

Nonlinear iterative inversion methods are computationally expensive, which leads to limited applications. In this paper, a fast algorithm of the cross-correlated contrast source inversion (CC-CSI) method is proposed. By assuming a homogeneous background medium, the task of solving systems of linear equations, the most time-consuming part of the CC-CSI method, has been efficiently implemented with several FFTs and IFFTs for transverse magnetic (TM), transverse electric (TE), and 3-D inversion, respectively. Theoretical analysis and real experiments demonstrate that the inversion efficiency of CC-CSI has been improved dramatically in comparison to the strategies of LU decomposition and the Biconjugate gradient algorithm. Specifically, the inversion speed of the proposed fast CC-CSI algorithm is at least one order of magnitude higher than using the latter two approaches in 3-D inversion, while the memory requirement of the proposed algorithm is intermediary and acceptable. Furthermore, the proposed fast scheme is also applicable to all the inversion methods which are related to computing of the electric fields directly from the contrast sources in homogeneous background media.

Analytical model for tension-induced residual stress of pre-stress filament hoop wound composite rings by inverse iteration method

Analytical model for tension-induced residual stress of pre-stress filament hoop wound composite rings by inverse iteration method

Machine-Learning-Based Deconvolution Method Provides High-Resolution Fast Inversion of Induction Log Data

We built a deconvolution model for induction log data using machine learning (ML). Unlike iterative forward modeling inversion methods, the deconvolution model is extremely fast. Unlike linear deconvolution models in the past, ML-based deconvolution finds accurate layer resistivity and layer boundaries. For a unit induction tool 2C40, the 21-point, 10-ft window deconvolution model works satisfactorily.