Inverse Reconstruction Method Research Articles

An optimized single-side inverse finite element method for displacement field reconstruction of wind turbine tower

Wind turbines are subjected to complex dynamic loads during actual operation, which are difficult to predict accurately in advance, which may lead to inaccurate structural strength assessment in the structural design stage, and thus bring safety risks to wind power towers. Inverse Finite Element Method (iFEM) is a reconstruction method of structural displacement distribution, which can estimate the full-field displacement distribution of tower, and used for structural on-line health monitoring. However, conventional iFEM require sensors to be placed on both sides of the structure, which greatly limits its engineering practicality. For this reason, a single-side inverse finite element (iFEM_S) was developed in this study to enhance the engineering applicability of iFEM. Both iFEM and iFEM_S are based on the principle of least squares variation, and the solution equations can be established when the measured strain is known. The core idea of iFEM_S is to find the optimal node displacement s to minimize the sum of mean square errors between the theoretical and measured strains on one side of the structure, thereby generating a set of algebraic equations. Solving these linear equations can achieve the structural displacement field. Additionally, A cyclic optimization algorithm (COA) was developed in this study to improve the robustness of reconstruction results through optimizing strain gauge locations, in which the condition number of pseudo stiffness matrix was used as the objective function, and the condition number is minimized, named iFEM_S_O. Finally, the reconstruction accuracy and robustness and of iFEM, iFEM_S and iFEM_S_O were verified through several numerical examples. The simulated reconstruction results indicated that iFEM_S_O is more accurate and stable than iFEM_S, and iFEM_S is more accurate and stable than iFEM.

Experimental validation of an inverse method for defect reconstruction in a two-dimensional waveguide model.

Defect reconstruction is essential in non-destructive testing and structural health monitoring with guided ultrasonic waves. This paper presents an algorithm for reconstructing notches in steel plates, which can be seen as artificial defects representing cracks by comparing measured results with those from a simulation model. The model contains a parameterized notch, and its geometrical parameters are to be reconstructed. While the algorithm is formulated and presented in a general notation, a special case of guided wave propagation is used to investigate one of the simplest possible simulation models that discretizes only the cross section of the steel plate. An efficient simulation model of the plate cross section is obtained by the semi-analytical scaled boundary finite element method. The reconstruction algorithm applied is gradient-based, and algorithmic differentiation calculates the gradient. The dedicated experimental setup excites nearly plane wave fronts propagating orthogonal to the notch. A scanning laser Doppler vibrometer records the velocity field at certain points on the plate surface as input to the reconstruction algorithm. Using two plates with notches of different depths, it is demonstrated that accurate geometry reconstruction is possible.

Surrogate Model of Solved Poisson Kriging Method for Radiation Field Reconstruction

Reverse reconstruction methods for the radiation field do not require information on the radioactive source and are capable of constructing the radiation field using a small amount of monitoring data, showing huge significance for radiation protection. However, in previous studies, inverse reconstruction methods have given less consideration to variations in the time dimension. Herein, the principle of the Poisson Kriging method solved by the surrogate model has been analyzed, and the Poisson Kriging method has been applied to the inverse reconstruction of two-dimensional radiation fields at different moments. On this basis, this work also investigated the effects of the principal function and correlation coefficient model on the objective function, the results of which demonstrate that the quadratic polynomial principal function and the Gaussian model correlation coefficient have good stability and convergence. Compared with the inverse distance weighting methods and the radial basis function methods, the Poisson Kriging method has smaller errors, showing that it is more suitable for reconstructing complex radiation fields. Finally, the Poisson Kriging method was applied to the Fukushima nuclear accident radiation field calculation. The Pearson correlation coefficient of its results was r = 0.49, reflecting the validity of this method. Our work provides a calculation method for the spatial distribution and trend of the radiation field in the early stages of a nuclear accident, which is helpful for furthering radiation protection and emergency responses to nuclear accidents.

An inverse method for curing process-induced eigenstrain reconstruction of laminated composites

Accurate acquisition of the curing process-induced eigenstrain distribution is vital for predicting residual stress of laminated composites. In this work we develop a novel inverse method for full-field PIE reconstruction of laminated composites. We design standard laminates to obtain the PIE of unidirectional and woven lamina which are key ingredients of full-field PIE. Then an inverse model is established to accurately calculate lamina’s PIE from the measured residual middle-plane strain and curvature of standard laminates. Full-field PIE of validation laminates are then reconstructed by the obtained lamina’s PIE. Experimental results are in good agreement with the reconstructed results, verifying the accuracy and effectiveness of our proposed method. Finally, we implement the inverse method in accurately reconstructing full-field PIE of a hybrid laminated composite I-beam. We also observe that the PIE is process dependent, indicating that PIE can be used to evaluate the effect of curing process on residual stress.

Predicting motions of deepwater platform based on the inverse reconstruction of environmental loads

In hybrid model testing technique, model tests are primarily used to verify numerical models which is used to predict the responses of full-depth systems. However, hybrid model testing method based on potential flow theory highly rely on the accuracy of mathematical model, facing challenges in accurately predicting full-depth responses with viscous effects, such as flow-induced motion. To solve the problem, a method for predicting motions of full-depth system is proposed based on the inverse reconstruction of the environmental loads from the truncated model test, considering viscous and nonlinear effects on platform. To validate the method, a series of model tests were conducted for a semi-submersible platform in head seas using both truncated and full-depth mooring systems to validate the method. The environmental loads could be extracted accurately via the inverse reconstruction method under different environmental conditions, including 100-year-return-period wave-only, current-only, coupled wave, wind, and current conditions. The results of time history, statistics, and power distribution show that the proposed method has better performance than conventional method of hybrid model test in situations where viscous effects are obvious.

Quantitative Optical Coherence Elastography: A Novel Intensity-Based Inversion Method Versus Strain-Based Reconstructions

Many diseases like cancer or atherosclerosis bear micro-scale tissue stiffness changes, which can be visualised by optical coherence elastography (OCE). OCE is a promising research field, where a growing number of publications present qualitative displacement maps. Quantitative OCE results have also been presented, but still lack high precision and good reproducibility, which are important for clinical applications. In this work, we compare three reconstruction methods for the Young's modulus in intensity-based quasi-static compressional OCE: uniaxial analysis, strain map based reconstruction facilitating a particle tracking improved optical flow (EOFM), and a novel image-based inverse reconstruction method (IIM). The quality of the proposed reconstruction methods is investigated by comparing their performance on twelve silicone elastomer phantoms with inclusions of varying size and stiffness. While the uniaxial reconstruction is strongly affected by lateral motion, EOFM is capable of deriving precise strain maps from consecutive OCT images during compression. However, for a valid Young's modulus reconstruction additional stress map information is required. IIM performs best, precisely reconstructing Young's modulus of inclusion and background, closely corresponding to separately determined ground truth values. The method offers a significant improvement of the relative error by a factor of 3.5 compared to uniaxial and strain-based analysis.

Inverse method for static load reconstruction with automatic filtering for optimal sensor placement

Inverse method for static load reconstruction with automatic filtering for optimal sensor placement

Study on airborne radar sea clutter suppression using deterministic space time model in post-Doppler domain

When the airborne radar observes the land or the sea scene, the echoes will contain a large of clutter. Therefore, the target detection will be influenced and the clutter suppression is necessary. The time varying sea clutter makes the detection of sea targets more difficult. However, the airborne radar sea clutter suppression is rarely studied. In this paper, the sea clutter suppression for single channel and multi-channel are studied, respectively. The Doppler domain localization (DDL) method is used to suppress the real sea clutter data measured with a single channel. The results show that we can choose proper range cell number in the post Doppler domain to get better sea clutter suppression performance. For the multi-channel sea clutter, the clutter suppression is executed using sample matrix inverse (SMI), cross spectral metric (CSM) methods, subspace projection method and the proposed inverse sample covariance matrix (SCM) reconstruction method in the post-Doppler domain with joint three Doppler channels. It can be found that the sea clutter can be cancelled effectively by CSM and inverse SCM reconstruction methods. The residual sea clutter is relatively more for the subspace projection method due to the inaccuracy of the projection matrix. The moving targets can be detected with SMI, CSM and inverse SCM reconstruction methods, while they are submerged in the sea clutter for the subspace projection method. Meanwhile, the minimal detectable velocity (MDV) curves under different sea states show that the detection performance of the slow moving targets deteriorates with the increase of the sea state. The results can provide effective support for airborne sea clutter suppression and sea target detection.

Effective reconstruction of bioluminescence tomography based on GPU-accelerated inverse Monte Carlo method

Diffusion equations (DEs) or simplified spherical harmonic equations are commonly used forward models in bioluminescence tomography (BLT), which are usually numerically calculated by the finite element method to construct the system matrix for reconstruction. However, the numerical solver is not accurate enough. The Monte Carlo (MC) method is regarded as the golden standard for modeling light propagation in biological tissue. In this paper, we proposed a GPU-accelerated inverse MC method for BLT reconstruction. The main feature is that the system matrix for BLT reconstruction is calculated by the MC method instead of the model-based numerical approximation. We evaluated the performance of the proposed method with both phantom-based simulation and animal-based in vivo experiment. The results show that, compared with the DE-based method, the proposed GPU-accelerated inverse MC method is more accurate and effective in BLT reconstruction.

Influence of self-absorption on reconstruction accuracy for temperature and concentration profiles of soot and metal-oxide nanoparticles in asymmetric nanofluid fuel flames

The inverse reconstruction method for the simultaneous estimation of temperature and concentration fields of soot and metal-oxide nanoparticles in asymmetric nanofluid fuel flame was improved by considering the self-absorption. The correction method to deal with the self-absorption in axisymmetric sooting flame for obtaining the unattenuated radiation intensity from the attenuated one detected by CCD camera was successfully extended to apply in asymmetric nanofluid fuel flame. These combustion parameters distributions can be concurrently deduced from the knowledge of the unattenuated radiation intensity using least-square QR (LSQR) decomposition and iterative methods. Self-absorption influences on the reconstruction accuracy in flames with different optical thicknesses were investigated and various levels of measurement errors were added into the simulation values from the practical experiment standpoint. The numerical results showed that the relative reconstruction errors of all the unknown parameters fields greatly reduced if self-absorption was considered in the reconstruction method. Moreover, as for the flame with larger optical thickness, the improvement of reconstruction accuracy was more significant.

Optimal Sensor Placement for Inverse Finite Element Reconstruction of Three-Dimensional Frame Deformation

The inverse finite element method (iFEM) for the 3D framework deformation reconstruction was introduced. As the process of iFEM did not require a priori knowledge, such as the modal shape, the loading, and the elastic-inertial material information of the structure, it presented high potential in the framework deformation reconstruction. With the current research, it was observed that the key step in the deformation reconstruction of the frame structure with iFEM was the section strains computing of the beam element from the surface strain measurements. The corresponding stability was severely affected by the placement of strain sensors. Therefore, it was necessary to discover a suitable sensor placement to maintain the stability of section strains computing. For this problem, one optimal model of sensor placement was proposed in this paper. Firstly, the well-separated eigenvalues were applied as the optimization target to construct the optimal model. Following, an optimal sensor placement was obtained through the optimal placement model solution, with the particle swarm optimization (PSO) method. Finally, the effectiveness of optimal placement was verified though the accuracy comparison of iFEM deformation reconstruction of a wing-like frame subjected to various loads for different schemes of sensor placement.

FEM-based elasticity reconstruction using ultrasound for imaging tissue ablation.

Success of ablation treatment depends on the accurate placement of the target ablation focus and the complete destruction of the pathological tissue. Thus, monitoring the formation, location, and size of the ablated lesion is essential. As ablated tissue gets stiffer, an option for ablation monitoring is ultrasound elastography, for imaging the tissue mechanical properties. Reconstruction of elasticity distribution can be achieved by solving an inverse problem from observed displacements, based on a deformable tissue model, commonly discretized by the finite element method (FEM). However, available reconstruction techniques are prone to noise and may achieve suboptimal accuracy. We propose a novel inverse problem formulation and elasticity reconstruction method, in which both the elasticity parameters and the model displacements are estimated as independent parameters of an unconstrained optimization problem. Total variation regularization of spatial elasticity distribution is introduced in this formulation, providing robustness to noise. Our approach was compared to state of the art direct and iterative harmonic elastography techniques. We employed numerical simulation studies using various noise and inclusion contrasts, given multiple excitation frequencies. Compared to alternatives, our method leads to a decrease in RMSE of up to 50% and an increase in CNR of up to 11dB in numerical simulations. The methods were also compared on an ex vivo bovine liver sample that was locally subjected to ablation, for which improved lesion delineation was obtained with our proposed method. Our method takes [Formula: see text] for [Formula: see text] reconstruction grid. We present a novel FEM problem formulation that improves reconstruction accuracy and inclusion delineation compared to currently available techniques.

Inverse method for hydrodynamic load reconstruction on a flexible surface-piercing hydrofoil in multi-phase flow

An inverse method for reconstruction of the in situ steady-state hydrodynamic load distribution using limited strain measurements is developed and validated on a rectangular, flexible surface-piercing hydrofoil in fully-wetted (FW) and fully-ventilated (FV) flows. The hydrofoil is used as a canonical proxy to more complex hydrodynamic lifting surfaces such as marine propulsors and turbines. The approach involves using a forward fluid–structure interaction (FSI) model to predict the hydroelastic response for given operating conditions. The inverse problem is solved as an optimization problem to determine unknown operating conditions. The forward FSI model consists of a nonlinear lifting line (LL) fluid solver with considerations for free surface, ventilation, and viscous effects, and a solid finite element method (FEM) solver using 1-D beam elements representing the spanwise bending and twisting deformations.The coupled FSI model was validated using data collected during towing tank experiments at the University of Michigan. Predictions of the lift and moment coefficients, as well as spanwise bending and twisting deformations agreed well with experimental results in FW and in FV flows.The inverse problem is formulated as an optimization problem to determine the unknown operating conditions that will minimize the difference between the measured and predicted deformations. To avoid non-uniqueness problems often encountered by inverse problems, a dynamic constraint using the measured wetted natural frequencies was added to help regularize the problem and speed up the solution process. A sequential quadratic programming algorithm was used as the optimizer for the inverse problem. The experimental studies showed that the inverse FSI model accurately determined the unknown operating conditions (angle of attack and immersed aspect ratio) for a given a known flow speed and a limited number of strain measurements in both FW and FV conditions. The converged results were used to reconstruct a 3-D hydrodynamic load distribution on the foil and to predict the cavity shape for FV operating conditions, which were found to agree well with experimental measurements and observations.

Inverse Scattering for Monochromatic Phaseless Measurements

An inverse method and measurement setup for profile and constitutive parameters reconstruction from monochromatic phaseless information is presented. The method is based on the minimization of a cost function that relates the measured field with the one scattered by a model of the object under test (OUT), where the position, contour, and constitutive parameters are the unknowns. As a result, phaseless information is directly related to the inverse problem unknowns, thus avoiding the need of an intermediate phase retrieval step. Due to the nonlinear nature of the cost function, global optimization techniques, such as the particle swarm optimization and differential evolution algorithms, have been considered for cost function minimization. An exhaustive analysis of the cost function behavior as a function of the electric size of the OUT is presented, discussing the optimal OUT size where the proposed methodology provides accurate profile and constitutive parameters reconstruction. The proposed methodology is conceived to use it together with a simple, low-cost measurement setup for fast characterization of perfect electric conductor and dielectric objects. Measurement examples are presented aiming to prove the feasibility of the described measurement setup.

Reconstruction of surface flaw shape using reflection data of guided Rayleigh surface waves

The paper proposes an inverse reconstruction method for surface flaws in a 2-D half-space using guided Rayleigh waves. When a guided Rayleigh wave is sent toward the flaw area, the reflected wave signals are observed and recorded at the far field. From wave scattering theory, the displacement field of reflected wave is expressed by an integral over the unknown flaw surface concerning the total wave field. By introduction of Born approximation and far-field expressions of Green's function, it is found that the reflection coefficient in wavenumber domain is related to the unknown shape of the cavity by a spatial Fourier transform relation. Thus, the location and shape of unknown cavity can be established. Numerical examples are illustrated in the paper. The research can act as a basis for quantitative ultrasonic guided wave non-destructive inspection.

Magnetic Resonance Elastography: Measurement of Hepatic Stiffness Using Different Direct Inverse Problem Reconstruction Methods in Healthy Volunteers and Patients with Liver Disease.

The purpose of this study was to compare the mean hepatic stiffness values obtained by the application of two different direct inverse problem reconstruction methods to magnetic resonance elastography (MRE). Thirteen healthy men (23.2±2.1 years) and 16 patients with liver diseases (78.9±4.3 years; 12 men and 4 women) were examined for this study using a 3.0 T-MRI. The healthy volunteers underwent three consecutive scans, two 70-Hz waveform and a 50-Hz waveform scans. On the other hand, the patients with liver disease underwent scanning using the 70-Hz waveform only. The MRE data for each subject was processed twice for calculation of the mean hepatic stiffness (Pa), once using the multiscale direct inversion (MSDI) and once using the multimodel direct inversion (MMDI). There were no significant differences in the mean stiffness values among the scans obtained with two 70-Hz and different waveforms. However, the mean stiffness values obtained with the MSDI technique (with mask: 2895.3±255.8 Pa, without mask: 2940.6±265.4 Pa) were larger than those obtained with the MMDI technique (with mask: 2614.0±242.1 Pa, without mask: 2699.2±273.5 Pa). The reproducibility of measurements obtained using the two techniques was high for both the healthy volunteers [intraclass correlation coefficients (ICCs): 0.840-0.953] and the patients (ICC: 0.830-0.995). These results suggest that knowledge of the characteristics of different direct inversion algorithms is important for longitudinal liver stiffness assessments such as the comparison of different scanners and evaluation of the response to fibrosis therapy.

An approximate 3D inversion method for inversion of single-well induction-logging responses

Electromagnetic logging is a technique used to probe differences in electric conductivity around a measurement device. Electromagnetic logging while drilling can contribute to proactive geosteering to improve well placement in reservoirs because such measurements can serve as an indication for the structure of the surrounding geology. We have developed a novel way of predicting the 3D conductivity distribution around a drilling tool, based on the contrast-source inversion method, in which we have replaced the full integral-equation approach by the single spherical scatterer (SSS) approximation. The approximation took into account the dominant features of the diffusive electromagnetic field. This allowed for a substantial gain in computational speed and storage of the inversion method for reconstruction of the conductivity distribution. In view of the limited range of the electromagnetic probing, the overall reconstruction can be segmented in several local windows. This reduced the computational speed requirements and the storage requirements dramatically, while safeguarding the overall 3D character of reconstruction. We have synthesized 3D electromagnetic logging data using synthetic models and conductivity maps from a hydrocarbon North Sea reservoir model. Reconstructions were made for multiple source frequencies, and the results were compared with the results obtained from the Born approximation. We have observed that reconstruction based on the SSS approximation was superior to the one based on the Born approximation. Our algorithm helped us determine the feasibility of producing reconstructions of reservoir sections in a short time frame, which allows for real-time decision making during drilling operations.

A model-based regularized inverse method for ultrasonic B-scan image reconstruction

Ultrasonic B-scan imaging is affected by the acoustic diffraction and electrical effects in nondestructive testing (NDT), resulting in insufficient lateral and temporal resolution for defect characterization. The minimum mean squared error (MMSE) method can improve the resolution by inversing a linear imaging model, which takes the acoustic diffraction and electrical effects into account, and achieve higher resolution than the synthetic aperture focusing technique (SAFT). However, its computation efficiency and resolution improvement are unsatisfactory due to the hypothetical Gaussian distribution of defects. To overcome these problems, a model-based regularized inverse method for ultrasonic B-scan image reconstruction is proposed. Benefitting from the sparse distribution of defects in NDT applications, the proposed method formulates an inverse objective function composed of -norm as well as -norm, and the sparse reconstruction by a separable approximation (SpaRSA) algorithm is adopted to obtain the optimal solution. The performance of the proposed method is evaluated by B-scan imaging of two 0.3 mm steel wires conducted both in simulation and experiment. The results verify that the proposed method improves the lateral and temporal resolution simultaneously with high computation efficiency.

Inverse Shape Reconstruction of Inner Cavities Using Guided SH-Waves in a Plate

The paper proposes an inverse reconstruction method for inner cavities in a 2D plate using guided SH-waves. When a pure incident wave mode is sent toward the flaw area, reflected waves are observed at the far field due to mode conversion. From wave scattering theory, the reflected wave field is expressed by an integral over the unknown flaw surface concerning the total wave field. By the introduction of Born approximation and far-field expressions of Green’s function, it is found that the reflection coefficient for the mode of the same order as that of the incident mode is related to the unknown shape of the cavity by Fourier transform relations. By mathematical deduction, we show that if the basic (0th-order) symmetric and the 1st-order antisymmetric modes are used as incident waves, the locations and shapes of upper and lower boundaries of the cavity can be reconstructed. Numerical examples are illustrated in the paper, and a proper condition for applying this method is discussed. The research can act as a basis of nondestructive inspection for latent flaws within more complicated structures.

A smoothed inverse eigenstrain method for reconstruction of the regularized residual fields

A smoothed inverse eigenstrain method is developed for reconstruction of residual field from limited strain measurements. A framework for appropriate choice of shape functions based on the prior knowledge of expected residual distribution is presented which results in stabilized numerical behavior. The analytical method is successfully applied to three case studies where residual stresses are introduced by inelastic beam bending, laser-forming and shot peening. The well-rehearsed advantage of the proposed eigenstrain-based formulation is that it not only minimizes the deviation of measurements from its approximations but also will result in an inverse solution satisfying a full range of continuum mechanics requirements. The smoothed inverse eigenstrain approach allows suppressing fluctuations that are contrary to the physics of the problem. Furthermore, a comprehensive discussion is performed on regularity of the asymptotic solution in the Tikhonov scheme and the regularization parameter is then exactly determined utilizing Morozov discrepancy principle. Gradient iterative regularization method is also examined and shown to have an excellent convergence to the Tikhonov–Morozov regularization results.