Iterative Inversion Method Research Articles

Power iteration and inverse power iteration for eigenvalue complementarity problem

SummaryIn this paper, an inverse complementarity power iteration method (ICPIM) for solving eigenvalue complementarity problems (EiCPs) is proposed. Previously, the complementarity power iteration method (CPIM) for solving EiCPs was designed based on the projection onto the convex cone K. In the new algorithm, a strongly monotone linear complementarity problem over the convex cone K is needed to be solved at each iteration. It is shown that, for the symmetric EiCPs, the CPIM can be interpreted as the well‐known conditional gradient method, which requires only linear optimization steps over a well‐suited domain. Moreover, the ICPIM is closely related to the successive quadratic programming (SQP) via renormalization of iterates. The global convergence of these two algorithms is established by defining two nonnegative merit functions with zero global minimum on the solution set of the symmetric EiCP. Finally, some numerical simulations are included to evaluate the efficiency of the proposed algorithms.

Inversing heat flux boundary conditions based on precise integration FEM without iteration and estimation of thermal stress in FGMs

In this article, based on the precise integration finite element method, a non-iterative inverse method is proposed to inverse the heat flux boundary conditions for the thermo-mechanical problem in functionally graded materials. Comparing with general iterative inverse methods, the novel inverse method can directly obtain accurate inversed results by least square method without iteration. Furthermore, the precise integration method is utilized to obtain a stable and accurate solution. On the other hand, in order to improve the adaptability of the inverse method, the unknown heat flux boundary conditions are expanded by a series of compactly supported radial basis functions. Once the unknown heat flux boundary conditions are determined, the temperature and thermal stress distributions can be estimated as well. Several examples are discussed to investigate some factors such as the random measurement error, the position and number of measurement points and the bias on measurement points’ position and thermophysical parameters. Numerical results show that the proposed method has excellent efficiency and accuracy.

An iterative inversion method using transient electromagnetic data to predict water-filled caves during the excavation of a tunnel

The correct interpretation of full-space transient electromagnetic data has always constituted a critical safety problem during tunnel excavation projects. Targeting the interpretation of water-filled caves under narrow tunnel conditions, we have developed an iterative inversion method based on 3D finite-difference time-domain (FDTD) forward calculations and a direction algorithm. In total, 125 groups of 3D FDTD forward calculation results are analyzed to identify the correlations between the response data and the geometric conditions of the cave. A direction algorithm is established based on the correlations, thereby increasing the iterative inversion convergence speed. Using the proposed iterative inversion method, the location and volume of the water-filled cave in front of the tunnel face are successfully inverted. Through an iterative program, the inversion results of simulations involving the detection of water-filled caves under tunnel conditions are accurately analyzed, and the relative error is less than 10%. The application of the iterative inversion method to the Mingyue Mountain Tunnel project suggests that this method is capable of interpreting the size of water-filled caves and it is valid for a narrow tunnel face with only a single available measurement point. The proposed iterative inversion method can be used alone or in combination with other detection techniques, thereby providing engineers with a better early warning system for detecting water-filled caves in tunnels.

Volumetric quantitative optical coherence elastography with an iterative inversion method.

It is widely accepted that accurate mechanical properties of three-dimensional soft tissues and cellular samples are not available on the microscale. Current methods based on optical coherence elastography can measure displacements at the necessary resolution, and over the volumes required for this task. However, in converting this data to maps of elastic properties, they often impose assumptions regarding homogeneity in stress or elastic properties that are violated in most realistic scenarios. Here, we introduce novel, rigorous, and computationally efficient inverse problem techniques that do not make these assumptions, to realize quantitative volumetric elasticity imaging on the microscale. Specifically, we iteratively solve the three-dimensional elasticity inverse problem using displacement maps obtained from compression optical coherence elastography. This is made computationally feasible with adaptive mesh refinement and domain decomposition methods. By employing a transparent, compliant surface layer with known shear modulus as a reference for the measurement, absolute shear modulus values are produced within a millimeter-scale sample volume. We demonstrate the method on phantoms, on a breast cancer sample ex vivo, and on human skin in vivo. Quantitative elastography on this length scale will find wide application in cell biology, tissue engineering and medicine.

Shape Design of Cable-net for Parabolic Cylindrical Deployable Antenna

A method of cable-net shape design based on the equilibrium matrix method is proposed for a new parabolic cylindrical deployable antenna structure with fewer modules. And the inverse iteration method is adopted to find the shape of cable-truss structure with considering the truss deformation induced by cable tension. Firstly, the ideal geometrical configuration of the locally symmetric support cable is designed for the given truss. Then, the pretension distribution of the cable is solved by the equilibrium matrix method under the circumstance of the unchanged topology of cable-net structure, position of nodes and boundary condition. In addition, the inverse iteration method is adopted to find the shape of cable-truss structure. Finally, the validity of the method is verified by simulation analysis.

Optimal prosodic feature extraction and classification in parametric excitation source information for Indian language identification using neural network based Q-learning algorithm

Automatic language identification (LID) system has extensively recognized in a real world multilanguage speech specific applications. The formation speech is relying on the vocal tract area which explores the excitation source information for LID task. In this paper, LID system utilizes sub segmental, segmental and supra segmental features from Linear Prediction residual of speech signal, represents various native language speech excitation source information. The glottal flow derivative of speech signal is obtained through iterative adaptive inverse filtering method. Moreover, the prosodic features of speech signal are extracted using short time Fourier transform due to its capability to process non-stationary signals. Finally, the deep neural network based Q-learning (DNNQL) algorithm has been employed for identification of the class label for a specific language. Experimental validation of the proposed approach is carried out using Indian language recorded database. Finally, the proposed LID system approach is performing well with 97.3% accuracy compared to other machine learning based approaches.

Estimation of fracture weaknesses and integrated attenuation factors from azimuthal variations in seismic amplitudes

Seismic wave propagation in fractured reservoirs exhibits anisotropy and attenuation, which are in turn related to fracture properties (e.g., fracture density) and fluid parameters (e.g., moduli and viscosity). Based on the linear slip theory, stiffness parameters can be determined for fractured and dissipative rocks, from which integrated attenuation factors involving host-rock intrinsic attenuation and fracture-induced attenuation emerge. Using a simplified mathematical form for these stiffness parameters, a linearized mathematical relationship directly relating the reflection coefficient to fracture weaknesses and integrated attenuation factors is available. A two-step inversion approach, involving (1) an iterative damped least-squares algorithm to predict P- and S-wave moduli using seismic angle gathers along the fracture orientation azimuth and (2) an iterative inversion method to estimate fracture weaknesses and integrated attenuation factors from azimuthal amplitude differences, is examined. The objective function for the second step is constructed based on a Bayesian framework. Synthetic testing confirms that fracture weaknesses and integrated attenuation factors are stably determined from seismic amplitudes exhibiting a moderate signal-to-noise ratio. The approach is applied to a field data set from a fractured carbonate reservoir. We observe that geologically reasonable results of fracture weaknesses and integrated attenuation factors are obtained. We conclude that this estimation procedure provides a reliable tool in fracture prediction and inverted attenuation factors appear as additional proofs to identify fluid type in fractured reservoirs.

Two-parameter prestack seismic inversion of porosity and pore structure parameter of fractured carbonate reservoirs: Part 1 — Methods

Fractured zones in deeply buried carbonate hills are important because they often have better permeability resulting in prolific production than similar low-porosity rocks. Nevertheless, their detection poses great challenge to conventional seismic inversion methods because they are mostly low in acoustic impedance and bulk modulus, hardly distinguishable from high-porosity zones or mudstones. A proxy parameter of pore structure defined in a rock-physics model, the so-called Sun model, has been used for delineating fractured zones in which the pore structure parameter is relatively high, whereas the porosity is low in general. Simultaneous seismic inversion of the pore structure parameter and porosity proves to be difficult and nontrivial in practice. Although the pore structure parameter is well-defined at locations where density, P-, and S-velocity are known from logs, estimation of P- and S-velocity information, especially density information from prestack seismic data is rather challenging. A three-step iterative inversion method, which uses acoustic, gradient, and elastic impedance from angle-stacked seismic data as input to the rock-physics model for calculating porosity and bulk and shear pore structure parameters simultaneously, is proposed and implemented to solve this problem. The methodology is successfully tested with well logs and seismic data from a deeply buried carbonate hill in the Bohai Bay Basin, China.

Alternating iterative methods for solving tensor equations with applications

Recently, the alternating direction method of multipliers (ADMM) and its variations have gained great popularity in large-scale optimization problems. This paper is concerned with the solution of the tensor equation $\mathscr{A}\textbf {x}^{m-1}=\textbf {b}$ in which $\mathscr{A}$ is an m th-order and n-dimensional real tensor and b is an n-dimensional real vector. By introducing certain auxiliary variables, we transform equivalently this tensor equation into a consensus constrained optimization problem, and then propose an ADMM type method for it. It turns out that each limit point of the sequences generated by this method satisfies the Karush-Kuhn-Tucker conditions. Moreover, from the perspective of computational complexity, the proposed method may suffer from the curse-of-dimensionality if the size of the tensor equation is large, and thus we further present a modified version (as a variant of the former) turning to the tensor-train decomposition of the tensor $\mathscr{A}$ , which is free from the curse. As applications, we establish the associated inverse iteration methods for solving tensor eigenvalue problems. The performed numerical examples illustrate that our methods are feasible and efficient.

Multiparameter deblurring filter and its application to elastic migration and inversion

Different types of model parameters, such as the P- and S-wave velocities, can be coupled to one another in multiparameter seismic inversion. This coupling effect is not taken into account by the conventional approximation to the Hessian inverse for a single type of parameter, and so it can lead to a slow rate of convergence by an iterative inversion method. To solve this problem, we have developed a multiparameter deblurring filter that approximates the Hessian inverse. This filter takes into account the coupling between different parameters by using stationary local filters to approximate the submatrices of the Hessian inverse for the different types of parameters. The filters are calculated by matching the reference multiparameter migration images to their reference reflectivity models. Numerical tests with elastic migration and inversion indicate that the multiparameter deblurring filter not only reduces the footprint noise, balances the amplitude, and increases the resolution of the elastic migration images, but it also mitigates the crosstalk artifacts caused by the coupling effect. When used as a preconditioner, it also accelerates the convergence rate for elastic inversion.

Electromagnetic Forward and Inverse Algorithms for 3-D Through-Casing Induction Mapping of Arbitrary Fractures

This letter extends the axisymmetric version of the efficient forward and inverse algorithms to characterize and reconstruct arbitrary 3-D fractures in a cased borehole environment. We improve our previous hybrid distorted Born approximation and stabilized biconjugate gradient fast Fourier transform method as the 3-D forward modeling algorithm that can significantly reduce the computational cost in forward modeling. The bounding constraints and model parameter transformation functions are introduced to our previous axisymmetric variational Born iterative inverse method to effectively reconstruct 3-D fractures. Numerical results show orders of magnitude higher efficiency of the forward algorithm than the finite-element method, and the effectiveness of the inverse algorithm for through-casing 3-D fracture reconstruction.

Inversion of Multifrequency Data With the Cross‐Correlated Contrast Source Inversion Method

AbstractCross‐correlated contrast source inversion (CC‐CSI) is a nonlinear iterative inversion method that is proposed recently for solving the inverse scattering problems. In CC‐CSI, a cross‐correlated error is constructed and introduced to the cost functional, which improves the inversion ability when compared to the classical design of the cost functional by exploiting the mismatch between the data error and state error. In this paper, the multifrequency inversion for electromagnetic waves is considered and a multifrequency version of CC‐CSI is proposed. Numerical and experimental inversion results of both transverse magnetic and transverse electric polarization demonstrate that when multifrequency data are available, CC‐CSI still outperforms the multiplicative‐regularized CSI method in the inversion of more complicated scatterers.

Accelerating the T‐matrix approach to seismic full‐waveform inversion by domain decomposition

ABSTRACTA seismic variant of the distorted Born iterative inversion method, which is commonly used in electromagnetic and acoustic (medical) imaging, has been recently developed on the basis of the T‐matrix approach of multiple scattering theory. The distorted Born iterative method is consistent with the Gauss–Newton method, but its implementation is different, and there are potentially significant computational advantages of using the T‐matrix approach in this context. It has been shown that the computational cost associated with the updating of the background medium Green functions after each iteration can be reduced via the use of various linearisation or quasi‐linearisation techniques. However, these techniques for reducing the computational cost may not work well in the presence of strong contrasts. To deal with this, we have now developed a domain decomposition method, which allows one to decompose the seismic velocity model into an arbitrary number of heterogeneous domains that can be treated separately and in parallel. The new domain decomposition method is based on the concept of a scattering‐path matrix, which is well known in solid‐state physics. If the seismic model consists of different domains that are well separated (e.g., different reservoirs within a sedimentary basin), then the scattering‐path matrix formulation can be used to derive approximations that are sufficiently accurate but far more speedy and much less memory demanding because they ignore the interaction between different domains. However, we show here that one can also use the scattering‐path matrix formulation to calculate the overall T‐matrix for a large model exactly without any approximations at a computational cost that is significantly smaller than the cost associated with an exact formal matrix inversion solution. This is because we have derived exact analytical results for the special case of two interacting domains and combined them with Strassen's formulas for fast recursive matrix inversion. To illustrate the fact that we have accelerated the T‐matrix approach to full‐waveform inversion by domain decomposition, we perform a series of numerical experiments based on synthetic data associated with a complex salt model and a simpler two‐dimensional model that can be naturally decomposed into separate upper and lower domains. If the domain decomposition method is combined with an additional layer of multi‐scale regularisation (based on spatial smoothing of the sensitivity matrix and the data residual vector along the receiver line) beyond standard sequential frequency inversion, then one apparently can also obtain stable inversion results in the absence of ultra‐low frequencies and reduced computation times.

Inverse iteration algorithm for neutron depth profiling

This work is based on the method of Monte Carlo simulation and probabilistic inversion for neutron depth profiling. The depth and concentration distribution of boron in a silicon matrix material is calculated. According to NDP experimental configuration at CARR, the energy spectra of a standard sample (SRM2137) are measured and simulated using MCNP and Geant4 software, and the concentration-depth profile of boron in SRM2137 is obtained by adopting an inverse iteration method through MATLAB software. It is shown that the inverse iteration calculation for NDP is feasible.

Semi-Analytical Source Method for Reaction–Diffusion Problems

Estimation of thermal properties, diffusion properties, or chemical–reaction rates from transient data requires that a model is available that is physically meaningful and suitably precise. The model must also produce numerical values rapidly enough to accommodate iterative regression, inverse methods, or other estimation procedures during which the model is evaluated again and again. Applications that motivate the present work include process control of microreactors, measurement of diffusion properties in microfuel cells, and measurement of reaction kinetics in biological systems. This study introduces a solution method for nonisothermal reaction–diffusion (RD) problems that provides numerical results at high precision and low computation time, especially for calculations of a repetitive nature. Here, the coupled heat and mass balance equations are solved by treating the coupling terms as source terms, so that the solution for concentration and temperature may be cast as integral equations using Green's functions (GF). This new method requires far fewer discretization elements in space and time than fully numeric methods at comparable accuracy. The method is validated by comparison with a benchmark heat transfer solution and a commercial code. Results are presented for a first-order chemical reaction that represents synthesis of vinyl chloride.

A simple and efficient inversion approach for estimation of primaries, surface-related multiples, and wavelets

Multiples can strongly interfere with primaries if they are not properly handled. An estimation of primaries by sparse inversion (EPSI) method was previously proposed to overcome the inaccuracies in prediction-subtraction techniques. However, the application of the iterative inversion method for the estimation of primaries is limited by the convergence rate and algorithmic complexity, given the expensive computational cost per iteration. A robust EPSI (REPSI) method was recently proposed to eliminate the free parameters involved in the original EPSI method at the expense of employing a complicated spectral-projected gradient l1 (SPGl1) algorithm. In addition, wavelet variation between shots is seldom considered in multiple estimation. Using the feedback primary-multiple model, we propose a simple and efficient inversion approach to estimate primaries, surface-related multiples, and shot-constant and shot-variant wavelets, without any requirements on the subsurface model and assumptions on the wavelet. We ...

Form-control of shell structures generated from hanging models with target heights

Shell structures generated from hanging models have structurally efficient forms. Form-control of these shells, which aims to obtain structural forms with single- and multiple target heights due to some architectural requirements, is discussed in this article. First, the vector form intrinsic finite element method is applied to generate the equilibrium form of hanging membranes and thus shell structures. Subsequently, the form-control problem is discussed, which aims to generate a structural form subject to given target height constrains. By introducing the Local Linearization Method to adjust Young’s modulus of the initial structural model, a form-control strategy to generate the equilibrium structural form with a single target height is proposed. By introducing the Inverse Iteration Method to adjust the geometry of the initial model, a form-control strategy to generate the equilibrium structural form with several target heights is proposed. Moreover, to verify the effectiveness of the vector form intrinsic finite element method and form-control strategies, structural analyses and shell behavior assessment of these shells are conducted. These strategies are effective and efficient, which can help architects or engineers to determine structurally efficient geometries in the design process much more easily.

Form Follows Force: A theoretical framework for Structural Morphology, and Form-Finding research on shell structures

With the springing up of freeform architectures, the key problem to structural engineers is to generate structural forms with high structural efficiency subject to the architectural space constraints during the conceptual design process. In this research, a theoretical framework for Structural Morphology has been proposed, that provides an effective solution to the problem. To enrich the proposed framework, systematic Form-Finding research on shell structures is conducted.

Tuning Fractures With Dynamic Data

AbstractFlow in fractured porous media is crucial for production of oil/gas reservoirs and exploitation of geothermal energy. Flow behaviors in such media are mainly dictated by the distribution of fractures. Measuring and inferring the distribution of fractures is subject to large uncertainty, which, in turn, leads to great uncertainty in the prediction of flow behaviors. Inverse modeling with dynamic data may assist to constrain fracture distributions, thus reducing the uncertainty of flow prediction. However, inverse modeling for flow in fractured reservoirs is challenging, owing to the discrete and non‐Gaussian distribution of fractures, as well as strong nonlinearity in the relationship between flow responses and model parameters. In this work, building upon a series of recent advances, an inverse modeling approach is proposed to efficiently update the flow model to match the dynamic data while retaining geological realism in the distribution of fractures. In the approach, the Hough‐transform method is employed to parameterize non‐Gaussian fracture fields with continuous parameter fields, thus rendering desirable properties required by many inverse modeling methods. In addition, a recently developed forward simulation method, the embedded discrete fracture method (EDFM), is utilized to model the fractures. The EDFM maintains computational efficiency while preserving the ability to capture the geometrical details of fractures because the matrix is discretized as structured grid, while the fractures being handled as planes are inserted into the matrix grids. The combination of Hough representation of fractures with the EDFM makes it possible to tune the fractures (through updating their existence, location, orientation, length, and other properties) without requiring either unstructured grids or regridding during updating. Such a treatment is amenable to numerous inverse modeling approaches, such as the iterative inverse modeling method employed in this study, which is capable of dealing with strongly nonlinear problems. A series of numerical case studies with increasing complexity are set up to examine the performance of the proposed approach.

Lithospheric structure of the South China Sea and adjacent regions: Results from potential field modelling

This work aims to investigate the crustal and lithospheric mantle thickness of the South China Sea (SCS) and adjacent regions. The crust-mantle interface, average crustal density, and lithospheric mantle base are calculated from free-air gravity anomaly and topographic data using an iterative inversion method. We construct a three-dimensional lithospheric model with different hierarchical layers. The satellite-derived gravity is used to invert the average crustal density and Moho (crust-mantle interface) undulations. The average crustal density and LAB (lithosphere–asthenosphere boundary) depths are further adjusted by topographic data under the assumption of local isostasy. The average difference in Moho depths between this study and the seismic measurement results is <1.5 km. The results show that in oceanic regions, the Moho depths are 7.5–30 km and the LAB depths are 65–120 km. The lithospheric thickness of the SCS basin and the adjacent regions increases from the sea basin to the continental margin with a large gradient in the ocean-continent transition zones. The Moho depths of conjugate plots during the opening of SCS, Zhongsha Islands and Reed Bank, reveal the asymmetric spreading pattern of SCS seafloor spreading. The lithospheric thinning pattern indicate two different spreading directions during seafloor spreading, which changed from N-S to NW-SE after the southward transition of the spreading axis. The lithosphere of the SCS basin and adjacent regions indicate that the SCS basin is a young basin with a stable interior lithosphere.