Iterative Inversion Algorithm Research Articles

Inversion of Oil-Immersed Paper Resistivity in Transformer Based on Dielectric Loss Factor

The aging of the transformer oil-paper insulation distributes spatially, which results in changes in paper resistivity in different regions. This paper establishes an iterative inversion algorithm using the finite element method to calculate the oil-immersed paper resistivity in different regions of a transformer. This algorithm sets the transformer dielectric loss factor tan δ at low frequency, the dielectric parameters of the transformer oil as inputs and the oil-immersed paper resistivity as output. The resistivity obtained from inversion can be used as a reference to access the insulation state of the oil-paper insulation. This paper aims at achieving the nondestructive detection of the partial state of the oil-paper insulation.

On convergence of the inverse iteration algorithm for modified Prony method

On convergence of the inverse iteration algorithm for modified Prony method

Multi-wavelength multi-angle reflection tomography.

We have developed a reflection tomographic microscope in which the sample is reconstructed from different holograms recorded under various angles and wavelengths of incidence. We present an iterative inversion algorithm based on a rigorous modeling of the wave-sample interaction that processes all the data simultaneously to estimate the sample permittivity distribution. We show that using several wavelengths permits a significant improvement of the reconstruction, especially along the optical axis.

Structural total least squares algorithm for locating multiple disjoint sources based on AOA/TOA/FOA in the presence of system error

Single-station passive localization technology avoids the complex time synchronization and information exchange between multiple observatories, and is increasingly important in electronic warfare. Based on a single moving station localization system, a new method with high localization precision and numerical stability is proposed when the measurements from multiple disjoint sources are subject to the same station position and velocity displacement. According to the available measurements including the angle-of-arrival (AOA), time-of-arrival (TOA), and frequency-of-arrival (FOA), the corresponding pseudo linear equations are deduced. Based on this, a structural total least squares (STLS) optimization model is developed and the inverse iteration algorithm is used to obtain the stationary target location. The localization performance of the STLS localization algorithm is derived, and it is strictly proved that the theoretical performance of the STLS method is consistent with that of the constrained total least squares method under first-order error analysis, both of which can achieve the Cramer-Rao lower bound accuracy. Simulation results show the validity of the theoretical derivation and superiority of the new algorithm.

One-step data-domain least-squares reverse time migration

Least-squares reverse time migration (LSRTM) is an iterative inversion algorithm for estimating the broadband-wavenumber reflectivity model. Although it produces superior results compared with conventional reverse time migration (RTM), LSRTM is computationally expensive. We have developed a one-step LSRTM method by considering the demigrated and observed data to design a deblurring preconditioner in the data domain using the Wiener filter. For the Wiener filtering, we further use a stabilized division algorithm via the Taylor expansion. The preconditioned observed data are then remigrated to obtain a deblurred image. The total cost of this method is about two RTMs. Through synthetic and real data experiments, we see that one-step LSRTM is able to enhance image resolution and balance source illumination at low computational costs.

Iterative inversion of deformation vector fields with feedback control.

Often, the inverse deformation vector field (DVF) is needed together with the corresponding forward DVF in four-dimesional (4D) reconstruction and dose calculation, adaptive radiation therapy, and simultaneous deformable registration. This study aims at improving both accuracy and efficiency of iterative algorithms for DVF inversion, and advancing our understanding of divergence and latency conditions. We introduce a framework of fixed-point iteration algorithms with active feedback control for DVF inversion. Based on rigorous convergence analysis, we design control mechanisms for modulating the inverse consistency (IC) residual of the current iterate, to be used as feedback into the next iterate. The control is designed adaptively to the input DVF with the objective to enlarge the convergence area and expedite convergence. Three particular settings of feedback control are introduced: constant value over the domain throughout the iteration; alternating values between iteration steps; and spatially variant values. We also introduce three spectral measures of the displacement Jacobian for characterizing a DVF. These measures reveal the critical role of what we term the nontranslational displacement component (NTDC) of the DVF. We carry out inversion experiments with an analytical DVF pair, and with DVFs associated with thoracic CT images of six patients at end of expiration and end of inspiration. The NTDC-adaptive iterations are shown to attain a larger convergence region at a faster pace compared to previous nonadaptive DVF inversion iteration algorithms. By our numerical experiments, alternating control yields smaller IC residuals and inversion errors than constant control. Spatially variant control renders smaller residuals and errors by at least an order of magnitude, compared to other schemes, in no more than 10 steps. Inversion results also show remarkable quantitative agreement with analysis-based predictions. Our analysis captures properties of DVF data associated with clinical CT images, and provides new understanding of iterative DVF inversion algorithms with a simple residual feedback control. Adaptive control is necessary and highly effective in the presence of nonsmall NTDCs. The adaptive iterations or the spectral measures, or both, may potentially be incorporated into deformable image registration methods.

Efficient algorithm for principal eigenpair of discrete p-Laplacian

This paper is a continuation of the author’s previous papers [Front. Math. China, 2016, 11(6): 1379–1418; 2017, 12(5): 1023–1043], where the linear case was studied. A shifted inverse iteration algorithm is introduced, as an acceleration of the inverse iteration which is often used in the non-linear context (the p-Laplacian operators for instance). Even though the algorithm is formally similar to the Rayleigh quotient iteration which is well-known in the linear situation, but they are essentially different. The point is that the standard Rayleigh quotient cannot be used as a shift in the non-linear setup. We have to employ a different quantity which has been obtained only recently. As a surprised gift, the explicit formulas for the algorithm restricted to the linear case (p = 2) is obtained, which improves the author’s approximating procedure for the leading eigenvalues in different context, appeared in a group of publications. The paper begins with p-Laplacian, and is closed by the non-linear operators corresponding to the well-known Hardy-type inequalities.

Trapdoor function based on the Ring-LWE and applications in communications

The “strong trapdoor function for lattice” has been constructed by Daniele Micciancio and Chris Peikert in EUROCRYPT 2012, which is simple, efficient, and easy to implement. In this paper, we present a new trapdoor function based on “ring learning with errors” problem (Ring-LWE) on lattice, and simultaneously the corresponding efficient inverse algorithm is given which involves two sub-algorithms: the trapdoor inverse algorithm and the iterative inverse algorithm. Our trapdoor function for lattice based on Ring-LWE is simultaneously more simple and efficient because of the ring structure. In addition to these advantages, our algorithm extends the parameters, and this can make our trapdoor function have a wider choice of applications.

Data inversion method for dual-frequency Doppler lidar based on Fabry-Perot etalon quad-edge technique

In order to realize the accurate inversion of lidar data, the calibration method for the ratio of Fabry-Perot etalon (FPE) transmission to reflection curve is given, and the reliability of the method is verified by simulation test. The effective ratio of FPE transmission to reflection for the actual atmospheric detection is analyzed, and a nonlinear iterative algorithm for simultaneous inversion of wind field and backscatter ratio, as well as the specific iterative steps, initial value determination methods and corresponding error formula of parameters are proposed. The simulation results show that no matter whether the backscatter ratio Rβ is small or large, the iterative process is always convergent and the correct inversion results can be obtained. The value of Rβ has a great influence on the convergence rate of its own, but has little effect on the wind speed convergence rate. The smaller Rβ is, the faster convergence rate of Rβ is, vice versa. Error analysis inferred that under the shot-noise limit, the radial wind speed measurement error decreases rapidly with the increase of Rβ for 1 <Rβ < 2, decreases slowly with the increase of Rβ for Rβ > 2; if the total number of backscattering photons of 50,000 received by telescope is assumed, the backscatter ratio measurement error increases with the increase of Rβ; within the wind speed measurement dynamic range of ±25 m/s, the radial wind speed error is below 2m/s and the backscatter ratio relative error is less than 4.1% when 1.1 <Rβ < 10.

A New Inversion Method Based on Distorted Born Iterative Method for Grounded Electrical Source Airborne Transient Electromagnetics

A new iterative inversion algorithm is proposed to reconstruct the electrical conductivity profile in a stratified underground medium for the grounded electrical source airborne transient electromagnetic (GREATEM) system. In forward modeling, we simplify the mathematical expressions of the magnetic fields generated by a finite line source in the layered ground to semianalytical forms in order to save the computation time. The Frechet derivative is derived for the electromagnetic response at the receivers due to a small perturbation of the conductivity in a certain layer underground. The initial expression of the Frechet derivative has an expensive triple integral and contains the Bessel function in the integrand. It is simplified by partially eliminating the integration along the source line and deriving the analytical expression for the integration in the vertical direction inside the perturbed layer. In the inverse solution, we use the distorted Born iterative method (DBIM). This is the first time that the DBIM is applied to data measured by the GREATEM system. Besides, the forward and inverse procedures are carried out in the frequency domain and based on the Frechet derivative of a line source. We demonstrate the validity of our forward model, Frechet derivative, inverse model, and the precision as well as robustness of the inversion algorithm through numerical computation and comparisons. Finally, we apply the inversion algorithm to the measured data and compare the retrieved conductivity to the actual drilling data.

Inverse Kinematics for 6-DOF Serial Manipulators With Offset or Reduced Wrists via a Hierarchical Iterative Algorithm

It is still a challenge to accurately and efficiently solve inverse kinematics (IK) using six-degrees-of-freedom (DOF) serial manipulators with offset or reduced wrists, which is mainly due to the complex, highly nonlinear, and coupled IK equations. In order to solve this problem, an efficient IK algorithm called hierarchical iterative inverse kinematic algorithm (HIIKA) is proposed in this paper. This novel IK solution algorithm consists of two-level iterations. The first-level iteration can achieve accurate initial estimates through an extended heuristic iterative method that proposed in this paper. The second-level iteration calculates all joint angles based on the results of the first-level iteration. To evaluate the performance of the HIIKA, experiments were carried out with a six-DOF manipulator with a two-DOF reduced wrist. The results obtained demonstrate the advancement and excellence of the HIIKA in terms of its convergence, accuracy, computational efficiency, and multiple solutions. The HIIKA provides a new tool for the analysis and application of manipulators with offset or reduced wrists.

Two-dimensional regularized inversion of AMT data based on rotation invariant of Central impedance tensor

Considering the uncertainty of the electrical axis for two-dimensional audo-magnetotelluric (AMT) data processing, an AMT inversion method with the Central impedance tensor was presented. First, we present a calculation expression of the Central impedance tensor in AMT, which can be considered as the arithmetic mean of TE-polarization mode and TM-polarization mode in the two-dimensional geo-electrical model. Second, a least-squares iterative inversion algorithm is established, based on a smoothness-constrained model, and an improved <italic>L</italic>-curve method is adopted to determine the best regularization parameters. We then test the above inversion method with synthetic data and field data. The test results show that this two-dimensional AMT inversion scheme for the responses of Central impedance is effective and can reconstruct reasonable two-dimensional subsurface resistivity structures. We conclude that the Central impedance tensor is a useful tool for two-dimensional inversion of AMT data.

Post-stack high-resolution deconvolution using Cauchy norm regularization with FX filter weighting

High-resolution deconvolution can mathematically be viewed as a regularized inverse problem. Besides, the result of the high-resolution deconvolution is generally accepted as reflectivity series of the layered media. On the other hand, lateral continuity is frequently poorer than vertical resolution on post-stack seismic section after application of any high-resolution deconvolution. However, because of the ill-posed inherent of the deconvolution problem, the Cauchy norm regularization term, a non-quadratic prior-information is widely used to provide the stability and uniqueness of the problem. But, it does not provide adequate quality of deconvolution if the noise in the data is strong. In this study, a stable and high-resolution deconvolution of post-stack seismic data was accomplished by an iterative inversion algorithm incorporating the Cauchy norm regularization with FX filter weighting. Cauchy norm regularization was utilized to force the solution to a spikiness structure, while the effective random noise reduction was performed by using the FX filter. Applications to synthetic and real post-stack data showed that the resolution in the vertical direction and continuity in the lateral direction are better improved. Thus, we think that this process makes seismic sections obtained especially from thin layered sedimentary basins more interpretable.

An iterative inversion of weighted Radon transforms along hyperplanes

We propose iterative inversion algorithms for weighted Radon transforms RW along hyperplanes in . More precisely, expanding the weight into the series of spherical harmonics in θ and assuming that the zero order term we reduce the inversion of RW to solving a linear integral equation. In addition, under the assumption that the even part of W in θ (i.e. ) is close to , the aforementioned linear integral equation can be solved by the method of successive approximations. Approximate inversions of RW are also given. Our results can be considered as an extension to 3D of two-dimensional results of Kunyansky (1992 Inverse Problems 8 809–19), Novikov (2014 Mosc. Math. J. 14 807–23), Guillement and Novikov (2014 Inverse Problems Sci. Eng. 22 787–802). In our studies we are motivated, in particular, by problems of emission tomographies in 3D. In addition, we generalize our results to the case of dimension .

Modeling the polarized X-ray scattering from periodic nanostructures with molecular anisotropy.

There is a need to characterize nanoscale molecular orientation in soft materials, and polarized scattering is a powerful means to measure this property. However, few approaches have been demonstrated that quantitatively relate orientation to scattering. Here, a modeling framework to relate the molecular orientation of nanostructures to polarized resonant soft X-ray scattering measurements is developed. A variable-angle transmission measurement called critical-dimension X-ray scattering enables the characterization of the three-dimensional shape of periodic nanostructures. When this measurement is conducted at resonant soft X-ray energies with different polarizations to measure soft material nanostructures, the scattering contains convolved information about the nanostructure shape and the preferred molecular orientation as a function of position, which is extracted by fitting using inverse iterative algorithms. A computationally efficient Born approximation simulation of the scattering has been developed, with a full tensor treatment of the electric field that takes into account biaxial molecular orientation, and this approach is validated by comparing it with a rigorous coupled wave simulation. The ability of various sample models to generate unique best fit solutions is then analyzed by generating simulated scattering pattern sets and fitting them with an inverse iterative algorithm. The interaction of the measurement geometry and the change in orientation across a periodic repeat unit leads to distinct asymmetry in the scattering pattern which must be considered for an accurate fit of the scattering.

Obtaining the Preinverse of a Power Amplifier Using Iterative Learning Control

Telecommunication networks make extensive use of power amplifiers to broaden the coverage from transmitter to receiver. Achieving high power efficiency is challenging and comes at a price: the wanted linear performance is degraded due to nonlinear effects. To compensate for these nonlinear disturbances, existing techniques compute the pre-inverse of the power amplifier by estimation of a nonlinear model. However, the extraction of this nonlinear model is involved and requires advanced system identification techniques. We used the plant inversion iterative learning control algorithm to investigate whether the nonlinear modeling step can be simplified. This paper introduces the iterative learning control framework for the pre-inverse estimation and predistortion of power amplifiers. The iterative learning control algorithm is used to obtain a high quality predistorted input for the power amplifier under study without requiring a nonlinear model of the power amplifier. In a second step a nonlinear pre-inverse model of the amplifier is obtained. Both the nonlinear and memory effects of a power amplifier can be compensated by this approach. The convergence of the iterative approach, and the predistortion results are illustrated on a simulation of a Motorola LDMOS transistor based power amplifier and a measurement example using the Chalmers RF WebLab measurement setup.

A product-of-exponential-based robot calibration method with optimal measurement configurations

This article presents a systematic and practical calibration method for an industrial robot to improve its absolute accuracy. The forward kinematics is established based on the global product-of-exponential formula considering some practical constraints. An enhanced partial pose measurement technique is used to construct the linearized error model with only position measurement. All the kinematic parameters are identified via the linear least-squared iteration. The end effector errors are compensated by an inverse Jacobian iteration algorithm in the robot joint space. To suppress the influences of the measurement error, an improved sequential forward floating search algorithm is proposed to select an optimal subset of configurations from a large pool of measured poses based on the D-Optimality. The proposed algorithm is verified via simulations. The calibration method is validated by experiments on an industrial robot, showing that the absolute accuracy of the robot is improved about 10 times under a statistics sense after the calibration.

Characteristics in hypocenters of microseismic events due to hydraulic fracturing and natural faults: a case study in the Horn River Basin, Canada

For two to three decades, microseismic monitoring has been popular in the development of unconventional resources, because the fracture network generated by hydraulic fracturing mainly controls the productivity, and microseismic monitoring enables direct measurements for imaging the fracture network. Nevertheless, some refinements are required to make this method more practical. One challenge is to quantify the effects of pre-existing natural fractures for generating microseismic events. We determine the hypocenters of microseismic events occurring in a shale gas play in the Horn River Basin, Canada, and report several interesting spatial and temporal features of the hypocenter distributions. Automatic phase-picking is applied to waveform data recorded at 98 shallow buried three-component geophones, and phases thought to be from the same event are associated. The initial hypocenters of events are determined by iterative linear inversion algorithm then relocated using a double-difference algorithm, where relative travel time measurements are obtained with the waveform cross-correlation. We group events into many clusters based on fracking stages and their hypocenters, and then define the best-fitting plane of hypocenters for each cluster. Most strikes of the best-fitting planes are consistent with the direction of local horizontal stress maximum, indicating that hydraulic fracturing induces most microseismic events. However, the best-fitting planes of several clusters have strikes similar to those of pre-existing faults or fractures, indicating that pre-existing natural faults or fractures can affect the generation of microseismic events. In addition, some observations suggest that natural fractures can affect the temporal evolution of the spatial occurrence pattern of microseismic events. We observed specific migration patterns of microseismic events around known faults in the study area. Although further work is required for complete understanding of this phenomenon, our observations help elucidate the nature of microseismic generation.

Estimation of seismic velocities and gas hydrate concentrations: A case study from the Shenhu area, northern South China Sea

In the Shenhu area of the northern South China Sea (SCS), canyon systems and focused fluid flow systems increase the complexity of the gas hydrate distribution in the region. It also induces difficulties in predicting the hydrate reservoir characteristics and quantitatively evaluating reservoir parameters. In this study, several inversion methods have been executed to estimate the velocities of strata and gas hydrate concentrations along a profile in the Shenhu area. The seismic data were inverted to obtain the reflection coefficient of each stratum via a spectral inversion method. Stratigraphic horizons were then delineated by tracking the inverted reflectivities. Based on the results of spectral inversion, a low-frequency velocity field of the strata was constructed for acoustic impedance inversion. Using a new iterative algorithm for acoustic impedance inversion, reflection coefficients were converted into velocities, and the velocity variations of the strata along a 2D seismic line were then obtained. Subsequently, gas hydrate saturations at well SH2 were estimated via the shale-corrected resistivity method, the chloride ion concentration method and three different rock physics models. The results were then compared to determine the optimal rock physics model, and the modified Wood equation (MWE) was found to be appropriate for this area. Finally, the inverted velocities and MWE were used to predict the distribution and concentrations of gas hydrates along the seismic line. The estimated spatial distribution of gas hydrates is consistent with that from sonic logging and resistivity data at well SH2, and with the drilling results. Therefore, this method is applicable in areas with no well data, or with few wells, and provides an effective tool for predicting and evaluating gas hydrates using seismic data.

Numerical and experimental identification of simplified building walls using the reflective Newton method

This article aims to present the coupling of a direct thermal calculation with an optimization algorithm to identify the thermal characteristics of a simplified building wall. The resolution of the direct thermal calculation is first based on an electric network representation that is numerically solved with a finite difference method. The optimization model minimizes a criterion, such as least squares, between the expected temperatures inside the building and the model response using a reflective Newton inverse iterative algorithm. The proposed optimization method is validated using an experimental study of a cubic wooden structure under controlled ambient conditions and a uniform heat source.