Proposed Inversion Algorithm Research Articles

F region electron density profile inversion from backscatter ionogram based on international reference ionosphere

Ionospheric backscatter sounding transmits HF (3–30MHz) radio wave obliquely into ionosphere and receives echoes backscattered from remote ground. Due to the focusing effect, the echoes form leading edge on the swept frequency backscatter ionogram (BSI). This kind of backscatter ionogram contains plentiful ionospheric information, such as electron density, radio wave propagation modes and maximum usage frequency (MUF). By inversion algorithm, the backscatter ionogram can provide two-dimensional electron density profile (EDP) down range. In this paper, we propose an ionospheric F2 region EDP inversion algorithm. By utilizing the F2 bottomside electron density profile represented by the International Reference Ionosphere (IRI) model and ray tracing techniques, this approach inverts the leading edge of the backscatter ionogram to two dimensional F region EDP. Results of validation experiments demonstrate that the inverted ionospheric EDPs show good agreement with the results of vertical ionosonde and provide reliable information of ionosphere. Thus the proposed inversion algorithm provide an effective and accurate method for achieving large scale and remote ionospheric electron density structure.

Compressive Hyperspectral Imaging With Side Information

A blind compressive sensing algorithm is proposed to reconstruct hyperspectral images from spectrally-compressed measurements.The wavelength-dependent data are coded and then superposed, mapping the three-dimensional hyperspectral datacube to a two-dimensional image. The inversion algorithm learns a dictionary {\em in situ} from the measurements via global-local shrinkage priors. By using RGB images as side information of the compressive sensing system, the proposed approach is extended to learn a coupled dictionary from the joint dataset of the compressed measurements and the corresponding RGB images, to improve reconstruction quality. A prototype camera is built using a liquid-crystal-on-silicon modulator. Experimental reconstructions of hyperspectral datacubes from both simulated and real compressed measurements demonstrate the efficacy of the proposed inversion algorithm, the feasibility of the camera and the benefit of side information.

Pulsatile arterial wall-blood flow interaction with wall pre-stress computed using an inverse algorithm.

BackgroundThe computation of arterial wall deformation and stresses under physiologic conditions requires a coupled compliant arterial wall-blood flow interaction model. The in-vivo arterial wall motion is constrained by tethering from the surrounding tissues. This tethering, together with the average in-vivo pressure, results in wall pre-stress. For an accurate simulation of the physiologic conditions, it is important to incorporate the wall pre-stress in the computational model. The computation of wall pre-stress is complex, as the un-loaded and un-tethered arterial shape with residual stress is unknown. In this study, the arterial wall deformation and stresses in a canine femoral artery under pulsatile pressure was computed after incorporating the wall pre-stresses. A nonlinear least square optimization based inverse algorithm was developed to compute the in-vivo wall pre-stress.MethodsFirst, the proposed inverse algorithm was used to obtain the un-loaded and un-tethered arterial geometry from the unstressed in-vivo geometry. Then, the un-loaded, and un-tethered arterial geometry was pre-stressed by applying a mean in-vivo pressure of 104.5 mmHg and an axial stretch of 48% from the un-tethered length. Finally, the physiologic pressure pulse was applied at the inlet and the outlet of the pre-stressed configuration to calculate the in-vivo deformation and stresses. The wall material properties were modeled with an incompressible, Mooney-Rivlin model derived from previously published experimental stress-strain data (Attinger et al., 1968).ResultsThe un-loaded and un-tethered artery geometry computed by the inverse algorithm had a length, inner diameter and thickness of 35.14 mm, 3.10 mm and 0.435 mm, respectively. The pre-stressed arterial wall geometry was obtained by applying the in-vivo axial-stretch and average in-vivo pressure to the un-loaded and un-tethered geometry. The length of the pre-stressed artery, 51.99 mm, was within 0.01 mm (0.019%) of the in-vivo length of 52.0 mm; the inner diameter of 3.603 mm was within 0.003 mm (0.08%) of the corresponding in-vivo diameter of 3.6 mm, and the thickness of 0.269 mm was within 0.0015 mm (0.55%) of the in-vivo thickness of 0.27 mm. Under physiologic pulsatile pressure applied to the pre-stressed artery, the time averaged longitudinal stress was found to be 42.5% higher than the circumferential stresses. The results of this study are similar to the results reported by Zhang et al., (2005) for the left anterior descending coronary artery.ConclusionsAn inverse method was adopted to compute physiologic pre-stress in the arterial wall before conducting pulsatile hemodynamic calculations. The wall stresses were higher in magnitude in the longitudinal direction, under physiologic pressure after incorporating the effect of in-vivo axial stretch and pressure loading.

Shape identification problems on detecting of defects in a solid body using inverse heat conduction approach

In this paper, a new shape identification method in the inverse heat conduction problem (IHCP) is applied to detect the location and size of defects in a solid body. Different defects are modeled in a solid body as an elliptical geometry whose parameters are estimated with a proposed inverse algorithm. The inverse algorithm consists of direct, inverse analysis, and gradient-based optimization method. The direct analysis is used a finite-element method in an unstructured grid system to solve the direct heat conduction problem. The inverse analysis is based on recording temperatures data on surface of solid body that calculates the objective function. The employed gradient-based optimization method is constructed using the adjoint, sensitivity, and conjugate gradient method (Powell-Beal’s version) that are used to calculate the gradient of objective function, step size, and minimizing the objective function, respectively. The effects of different noisy temperature data, different cavities on some domains, and different type of defects such as poor cure, porosity, and crack are investigated in this work. The results show that this proposed inverse algorithm is more efficient in detection of defects.

Quantitative evaluation of thermal barrier coating based on eddy current technique

Thermal Barrier Coating (TBC), as the insulation between high-temperature gas and the alloying bodies of gas turbine blades, is adopted for protection and long-term service of gas turbines. It is imperative to non-destructively evaluate TBC of blades, since the TBC with thin thickness or delamination will lead to catastrophic accidents of gas turbines. In this paper, Eddy Current inspection (EC) is proposed for quantitative evaluation of TBC, which involves estimation of: (1) thickness of the top coating to identify possible thinning and (2) thickness and conductivity of bond coating to detect delamination and degradation. In an effort to implement the fast inversion, the closed-form expressions of the Jacobian matrix are derived based on Truncated Region Eigenfunction Expansion (TREE) modeling. The Levenberg–Marquardt (LM) algorithm is also adopted in the inversion for the parameters. The proposed inverse algorithm is verified by hybrid numerical modeling and experiments, which indicates that the quantitative evaluation of TBC by using EC in conjunction with the proposed inverse algorithm is valid and applicable to the engineering application.

Self-tuning distributed measurement fusion Kalman estimator for the multi-channel ARMA signal

For the multisensor multi-channel autoregressive moving average (ARMA) signal with white measurement noises and a common disturbance measurement white noise, when the model parameters and the noise variances are all unknown, a multi-stage information fusion identification method is presented, where the consistent fused estimates of the model parameters and noise variances are obtained by the multi-dimension recursive instrumental variable (RIV) algorithm, correlation method and Gevers–Wouters algorithm with a dead band. Substituting these estimates into the optimal distributed measurement fusion Kalman signal estimator, a self-tuning distributed measurement fusion Kalman signal estimator is presented. Its convergence is proved by the dynamic error system analysis (DESA) method, so that it has asymptotical global optimality. In order to reduce computational load, a fast recursive inversion algorithm for a high-dimension matrix is presented by the inversion formula of partitioned matrix. Especially, when the process and measurement noise variance matrices are all diagonal matrices, the inversion formula of a high-dimension matrix is presented, which extends the formula of the inverse of Pei–Radman matrix. Applying the proposed inversion algorithm, the computation of the fused measurement and fused noise variance is simplified and their computational burden is reduced. A simulation example shows effectiveness of the proposed method.

Robust Full Waveform Inversion Using Normalized Residual in the Frequency Domain

ABSTRACT A robust objective function for the full waveform inversion has been suggested in the frequency domain. The proposed objective function is defined as sum of complex absolute values of residual wavefields in the frequency domain. Generally, the full waveform inversion is extremely sensitive to the parameterization, frequency bandwidth, attenuation, noise and so on. Especially, noise is the most important factor in the full waveform inversion. In the frequency-domain waveform inversion, the attenuation of wavefields is one of the critical parameters for successful inversion. To verify the robustness of our algorithm, the proposed inversion scheme was tested in terms of the sensitivity to attenuation and noise. The comparison examples with both the conventional l 2-norm and the logarithmic objective function demonstrated that the proposed inversion algorithm is robust to noise and less sensitive to attenuation.

Near-infrared frequency domain system and fast inverse Monte Carlo algorithm for endoscopic measurement of tubular tissue

A near infrared diffuse reflectance system for endoscopic measurement and an inverse algorithm for extracting optical properties of tubular tissues were developed in this paper. The measurement system worked in the frequency domain mode and a custom probe was employed for endoscopic detection of cervical cancer. Experiments for evaluating the measurement accuracy indicate that the model-to-data mismatch for the AC amplitude and phase lag is less than 3.7% and 6.7%, respectively. To facilitate the extraction of the optical properties in tubular tissues and to minimize the influence of the initial guess on the reconstruction accuracy, a fast inverse Monte Carlo simulation algorithm with cluster analysis method was proposed. Simulation results showed that the relative errors of the absorption coefficient recovered using the proposed inverse algorithm are less than 5.8% and those of the sacttering coefficient are less than 10.2%. Endoscopic measurement on two tubular solid phantoms were also carried out to evaluate the system and the inversion scheme. The results demonstrated that less than 20% relative error can be achieved.

5D seismic data regularization by a damped least-norm Fourier inversion

Regularizing inadequate and irregularly sampled seismic data is one of important problems in seismic data processing. An improvement to existing methods to solve this problem is proposed by applying a 5D regularization/interpolation scheme with a damped least-norm Fourier inversion. Under the assumption of planar seismic events within small data windows, the spatial spectrum of regularized data for a fixed frequency should be sparse and have minimum damped norm. The inversion scheme consists in finding a set of regularly spaced spatial Fourier coefficients by minimizing its damped norm for each frequency, subject to the condition that the resulting spatial Fourier coefficients also faithfully reconstruct the original data. The damping factors are automatically derived from the amplitude spectra of the regularized low-frequency data. With the guidance of the damping factors and automatic adjustment of wavenumber ranges according to the Nyquist sampling theory, the proposed inversion algorithm naturally yields a one-step solution for both stabilization and antialiasing of the interpolation problem. A distinctive feature of the method is that it uses high-dimensional nonuniform fast Fourier transforms to evaluate expensive discrete Fourier transforms involved in conjugate gradient iterations. This improves the computational efficiency. The results of applying this algorithm to synthetic and field data demonstrate that it performs well when applied to highly irregular data and outperforms lower dimensional interpolation schemes.

Particle sizing in dense two-phase droplet systems by ultrasonic attenuation and velocity spectra

Size and size distribution of particles in particulate two-phase flow play an important role in a wide variety of industrial areas, while their measurement still remains a hard task till now. Ultrasonic wave as a mechanical vibration contains plenty of information about medium when it passes through. Thus the size distribution could be extracted from the measured ultrasonic attenuation and velocity spectra by means of well established models and data processing techniques. This paper contributes to the extraction of information of droplet size of a two-phase fat emulsion simultaneously from signals of broad-band ultrasonic attenuation and velocity spectra. According to the formulated single particle scattering model, the relationship between particle size distribution and ultrasonic spectrum is established. The sensitivities of ultrasonic spectra to the variation of particle size are illustrated. Distinguishing features for attenuation and velocity spectra are summarized. Demonstration calculations of inversion by optimum regularization factor method are carried out to yield the typical numerical results for discussion. Based on the proposed inversion algorithm and theoretical model, a fat emulsion sample with a volume fraction up to 20% is measured and analyzed. To validate the proposed ultrasonic spectrum particle sizing method, the results are compared to those obtained from optical measurement.

Hydrogeophysical Approach for Identification of Layered Structures of the Vadose Zone from Electrical Resistivity Data

The electric resistivity survey and borehole collection of resistivity data are one of the oldest geophysical tools for characterization of the vadose zone. A current trend is to conduct such surveys in a tomographic manner, which requires significant computational resources. We present a simple, semianalytical approach to delineate multiple layers in partially saturated soils from resistivity and saturation measurements taken at several depths along a borehole. The number of layers and their hydraulic properties are assumed to be known. The proposed inversion algorithm is computationally efficient and can serve either as a stand‐alone tool for layer delineation or as an autonomous module in a more comprehensive geophysical survey. It is most robust when each layer is sampled at least once. When one or more layers have not been sampled, the algorithm's robustness (convergence) depends on the accuracy of an initial guess (e.g., expert knowledge and other hard or soft data). We provide a detailed analysis of the algorithm's convergence and identify potential pitfalls.

A fast algorithm for inverse airfoil design using a transpiration model and an improved vortex panel method

A fast algorithm for inverse airfoil design using an efficient panel method for potential flow calculation is presented. The method employs linear vortex distributions on the panels and a consistent procedure for imposing the Kutta condition, thus eliminating the spurious aerodynamic loading that usually appears at a cusped trailing edge. The algorithm searches the airfoil ordinates attending to a given surface velocity distribution with fixed abscissas. It begins with a guessed starting shape and successively modifies it by an iterative process, such that the normal velocity vanishes and the calculated velocity distribution gradually approaches the required one. Each iteration is performed in two main steps: 1) the flow calculation step; 2) the geometrical marching step, where the calculated velocity distribution is compared with the required one and a transpiration model is applied to modify the current shape towards another one more close to the target shape. The geometrical marching is conducted by varying the panel slopes as a function of the normal velocity excess induced by the difference between the required and calculated velocities. A scheme is applied in order to close the body shape. Various test cases were carried out and are presented for the efficiency and robustness validation of the proposed inverse algorithm. Keywords : inverse method, panel method, airfoils, vortex distributions

An improved genetic local search algorithm for defect reconstruction from MFL signals

This paper presents an improved genetic local algorithm by incorporating the simulated-annealing technique into the perturbation process of the genetic local search algorithm and proposes an improved-genetic-local-search-algorithm-based inverse algorithm for two-dimensional defect reconstruction from the magnetic-flux-leakage signals. In the algorithm, a radial-basis-function neural network is utilized as a forward model, and the improved genetic local search algorithm is used to solve the optimization problem in the inverse problem. Experiments are presented to compare the proposed inverse algorithm with both the canonical-genetic-algorithm-based inverse algorithm and the genetic-local-search-algorithm-based inverse algorithm. The results demonstrate that the proposed inverse algorithm is more accurate and robust to the noise.

2D defect reconstruction from MFL signals by a genetic optimization algorithm

The magnetic flux leakage (MFL) method has established itself as the most widely used in-line inspection technique for the evaluation of gas and oil pipelines. An important problem in MFL nondestructive evaluation (NDE) is signal inverse problem, wherein the defect profile and its parameters are determined using the information contained in the measured signals. This paper proposes a genetic-algorithm-based inverse algorithm for reconstructing 2-D defect from MFL signals. In the algorithm, a radial basis function neural network (RBFNN) is used as forward model, and genetic algorithm is used to solve the optimization problem in the inverse problem. Experimental results are presented to demonstrate the effectiveness of the proposed inverse algorithm.

Identification methods in nonlinear heat conduction. Part II: inverse problem using a reduced model

A method for solving nonlinear Inverse Heat Conduction Problems (IHCPs) using a Reduced Model (RM) is proposed in this numerical study. In a first step, RM is identified through a specific procedure using optimization techniques and a Detailed Model (DM). Compared to DM, RM allows drastic reduction of computing time without significant loss of accuracy. The second step is the sequential resolution of the inverse problem using RM, taking into account data at Future Time Steps in order to estimate a time-varying thermal input from the knowledge of simulated temperature measurements inside the domain. A transient 3D example with thermal conductivity linearly dependant on temperature illustrates the method. It is shown, on this example, that the proposed inversion algorithm using a simple Euler implicit scheme in time gives good results with RM, whereas it does not work with DM.

Inversion of surface parameters from polarimetric SAR

Proposes a new model for the inversion of surface roughness and soil moisture from polarimetric synthetic aperture radar (SAR) data, based on the eigenvalues and eigenvectors of the polarimetric coherency matrix. It demonstrates how three polarimetric parameters, namely the scattering entropy (H), the scattering anisotropy (A), and the alpha angle (/spl alpha/) may be used in order to decouple surface roughness from moisture content estimation offering the possibility of a straightforward inversion of these two surface parameters. The potential of the proposed inversion algorithm is investigated using fully polarimetric laboratory measurements as well as airborne L-band SAR data and ground measurements from two different test sites in Germany, the Elbe-Auen site and the Weiherbach site.

Inverse scattering by penetrable objects in two-dimensional elastodynamics

In this paper, a method for the shape reconstruction of a penetrable scatterer in two-dimensional linear elasticity is presented. The direct scattering problem is formulated in a dyadic form, a fact that is enforced by the dyadic nature of the free-space Green's function. Approximate far-field equations with known terms the P and S parts of the fundamental dyadic solution at the radiation zone are used. The mathematical analysis presented is based on an interior transmission problem where a weak-type solution is introduced. The proposed inversion algorithm is an extension of the sampling method for the two-dimensional elastic case. The boundary of the scatterer can be found by noting that the L 2-norms of the Herglotz kernels of the approximate far-field equations are not bounded as the source point of the fundamental solution approaches the boundary from inside. Numerical results for penetrable objects are presented illustrating the applicability of this method.

Anisotropic parameter identification using inhomogeneous tensile test

In this contribution, an inverse identification strategy of constitutive laws for elastoplastic behaviour is presented. The proposed inverse algorithm is composed on an appropriate finite element calculation combined with an optimisation procedure. It is applied to identify material anisotropic coefficients using a set up of easy performed laboratory tests. The used experimental data are the plane tensile test and the off axes tensile tests. The identified behaviour models are mainly based on Hill's quadratic yield criterion. Two cases of this yield criterion have been considered: the transverse isotropic and the orthotropic one under an associated and non-associated flow rule assumptions for each case. The yield surface has been assumed to expand isotropically (isotropic strain hardening law) as a function of the plastic work. In order to better describe anisotropic plastic properties of the studied materials, a recently planar anisotropic yield function is used. It is a non-quadratic yield criterion which takes account of anisotropic yield stresses as well as anisotropic strain ratios. It is subsequently shown that the agreement between inverse identification results and experimental measurements were improved. We prove also that the presented strategy is a good alternative to the simplified homogeneous tests assumption, especially for the plane tensile test.

Geo-fit approach to the analysis of limb-scanning satellite measurements

We propose a new approach to the analysis of limb-scanning measurements of the atmosphere that are continually recorded from an orbiting platform. The retrieval is based on the simultaneous analysis of observations taken along the whole orbit. This approach accounts for the horizontal variability of the atmosphere, hence avoiding the errors caused by the assumption of horizontal homogeneity along the line of sight of the observations. A computer program that implements the proposed approach has been designed; its performance is shown with a simulated retrieval analysis based on a satellite experiment planned to fly during 2001. This program has also been used for determining the size and the character of the errors that are associated with the assumption of horizontal homogeneity. A computational strategy that reduces the large number of computer resources apparently demanded by the proposed inversion algorithm is described.

An inverse solution for finite journal bearings lubricated with couple stress fluids

This paper presents an inverse solution for finite journal bearings lubricated with couple stress fluids to estimate the eccentricity ratio and the couple stress parameter for a given experimentally measured pressure distribution. The least-squares optimization technique is used to solve the inverse problem. An efficient numerical scheme is developed to solve the direct lubrication problem, which consists of the modified Reynolds equation, the film thickness equation, and the boundary conditions for the pressure field. The flexibility of the bearing liner is considered in the film thickness equation by a simple elastic model. The proposed inverse algorithm was tested using numerically simulated pressure distribution. The results showed that as the percentage of random error added to the numerically calculated pressure data points increases, the number of iterations required for convergence increases slightly, and the accuracy of the predictions decreases especially in the case of elastic liner.