Nonlinear Inversion Approach Research Articles

Optical flow-based control for micro air vehicles: an efficient data-driven incremental nonlinear dynamic inversion approach

Optical flow-based control for micro air vehicles: an efficient data-driven incremental nonlinear dynamic inversion approach

2D boundary-condition-free nonlinear inversion technique applied to optical shear vibration induced microelastography

Optical microelastography (OME) has emerged as a new technique for quantifying cellular mechanical properties. However, accurately reconstructing viscoelastic properties at the microscale level from noisy 2D displacement fields remains a challenge. This study introduces a 2D boundary-condition-free nonlinear inversion (2D-NoBC-NLI) approach, addressing challenges of interpreting noisy data and deducing full-field 3D displacements from 2D measurements. OME requires vibrating the cell and mapping the shear modulus based on wave-induced displacements within the cell. The shear modulus distribution is recovered via a coupled adjoint field NLI reconstruction to allow 2D-NoBC-NLI. Validation was conducted through numerical simulations at 36 kHz on a homogeneous sphere of 75 μm diameter and an assigned viscoelastic modulus, G*, of 800 + i150 Pa. The same reconstruction approach was also applied to experimental data obtained from polyacrylamide (PAAm) microbeads of the same diameter. Results demonstrated relative differences from true simulated values of 0.7% and 45% for storage and loss moduli, respectively, with a coefficient of variation under 1% for homogeneous regions. When applying this method to PAAm microbeads, viscoelastic reconstructions showed the potential of OME under experimental conditions. These findings highlight the accuracy of 2D-No BC-NLI reconstruction in OME for precise microscale characterization and mapping of the viscoelastic cell structure.

Frequency-Dependent Nonlinear AVO Inversion for Q-Factors in Viscoelastic Media

Viscoelastic theory-based frequency-dependent amplitude variation with offset (AVO) inversions are a useful tool for identifying fluids based on their dispersion properties. When used to identify reservoir oil and gas qualities, the quality factors ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factors) derived from the inversion have produced good results. But currently, the majority of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor inversions are linear inversions based on linear approximations, whereas nonlinear inversions based on exact equations with higher precision and fewer assumptions are only occasionally carried out. Meanwhile, in broadband seismic inversion, the low-frequency model estimated by complex frequency inversion can fully utilize seismic data’s low-frequency information and provide improved robustness and rationality for inversion. Therefore, we derive a frequency-dependent reflection coefficient equation that varies with angle by replacing the nearly constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> model suggested by Aki and Richards into the exact Zoeppritz equation and simplifying. Additionally, using the Bayesian framework as a foundation, we created a novel two-stage broadband frequency-dependent nonlinear inversion approach for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factors that can estimate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factors, produce accurate fluid identification results, and serve as a solid foundation for oil and gas exploration and reservoir identification. Utilizing examples from both synthetic and real-world data, we verify the applicability of oil and gas indicators.

Pore Pressure Estimation for Shaly Sand Formations Using Rock Physics Models For Compressional and Shear Velocities: A 1D Geomechanical Approach

Pore pressure estimation in sedimentary basins has been made exclusively through the compressional velocity data since the 1960s, using the normal compaction trend and lithostatic pressure profile derived from wireline logs. Considering that seismic velocity is highly dependent on petrophysical parameters such as porosity and clay volume, pore pressure estimation is commonly associated with a high degree of uncertainty due to simplistic assumptions that neglect those dependencies. To improve that, we propose two empirical velocity models based on compressional and shear rock physics relations for pore pressure prediction in shaly sand formations. These formulations extend Bowers and Doyen formulae, linking compressional and shear velocities with effective stress and petrophysical parameters. Finally, we used a non-linear multidimensional inversion approach to calibrate the proposed models and apply them in the context of a 1D geomechanics and pore pressure prediction study of an upper cretaceous overpressured shaly sand oil reservoir. The results show good agreement with pore pressure data and pressure predictions from the traditional Eaton method. The advantage of the proposed approach is its consistency throughout the entire well-log petrophysical interpretation workflow, especially concerning porosity, clay volume and saturation.

Polarimetric radar reveals the spatial distribution of ice fabric at domes and divides in East Antarctica

Abstract. Ice crystals are mechanically and dielectrically anisotropic. They progressively align under cumulative deformation, forming an ice-crystal-orientation fabric that, in turn, impacts ice deformation. However, almost all the observations of ice fabric are from ice core analysis, and its influence on the ice flow is unclear. Here, we present a non-linear inverse approach to process co- and cross-polarized phase-sensitive radar data. We estimate the continuous depth profile of georeferenced ice fabric orientation along with the reflection ratio and horizontal anisotropy of the ice column. Our method approximates the complete second-order orientation tensor and all the ice fabric eigenvalues. As a result, we infer the vertical ice fabric anisotropy, which is an essential factor to better understand ice deformation using anisotropic ice flow models. The approach is validated at two Antarctic ice core sites (EPICA (European Project for Ice Coring in Antarctica) Dome C and EPICA Dronning Maud Land) in contrasting flow regimes. Spatial variability in ice fabric characteristics in the dome-to-flank transition near Dome C is quantified with 20 more sites located along with a 36 km long cross-section. Local horizontal anisotropy increases under the dome summit and decreases away from the dome summit. We suggest that this is a consequence of the non-linear rheology of ice, also known as the Raymond effect. On larger spatial scales, horizontal anisotropy increases with increasing distance from the dome. At most of the sites, the main driver of ice fabric evolution is vertical compression, yet our data show that the horizontal distribution of the ice fabric is consistent with the present horizontal flow. This method uses polarimetric-radar data, which are suitable for profiling radar applications and are able to constrain ice fabric distribution on a spatial scale comparable to ice flow observations and models.

Evaluation of cerebral cortex viscoelastic property estimation with nonlinear inversion magnetic resonance elastography

Objective. Magnetic resonance elastography (MRE) of the brain has shown promise as a sensitive neuroimaging biomarker for neurodegenerative disorders; however, the accuracy of performing MRE of the cerebral cortex warrants investigation due to the unique challenges of studying thinner and more complex geometries. Approach. A series of realistic, whole-brain simulation experiments are performed to examine the accuracy of MRE to measure the viscoelasticity (shear stiffness, μ, and damping ratio, ξ) of cortical structures predominantly effected in aging and neurodegeneration. Variations to MRE spatial resolution and the regularization of a nonlinear inversion (NLI) approach are examined. Main results. Higher-resolution MRE displacement data (1.25 mm isotropic resolution) and NLI with a low soft prior regularization weighting provided minimal measurement error compared to other studied protocols. With the optimized protocol, an average error in μ and ξ was 3% and 11%, respectively, when compared with the known ground truth. Mid-line structures, as opposed to those on the cortical surface, generally display greater error. Varying model boundary conditions and reducing the thickness of the cortex by up to 0.67 mm (which is a realistic portrayal of neurodegenerative pathology) results in no loss in reconstruction accuracy. Significance. These experiments establish quantitative guidelines for the accuracy expected of in vivo MRE of the cortex, with the proposed method providing valid MRE measures for future investigations into cortical viscoelasticity and relationships with health, cognition, and behavior.

Nonlinear Waveform Inversion for Quantitative Ultrasound

Due to its non-invasive and non-radiating nature, along with its low cost, ultrasound (US) imaging is widely used in medical applications. Typical B-mode US images have limited resolution and contrast and weak physical interpretation. Inverse US methods were developed to reconstruct the media's speed-of-sound (SoS) based on a linear acoustic model. However, the wave propagation in medical US is governed by nonlinear acoustics, which introduces more complex behaviors neglected in the linear model. In this work we propose a nonlinear waveform inversion (NWI) approach for quantitative US, that considers a nonlinear acoustics model to simultaneously reconstruct multiple material properties, including the medium's SoS, density, attenuation, and nonlinearity parameter. We thus broaden current inverse US approaches, such as the full waveform inversion (FWI) algorithm, by considering nonlinear media, and additional physical parameters. We represent the nonlinear acoustic model by means of a recurrent neural network, which enables us to apply advanced optimization algorithms borrowed from the deep learning toolbox and achieve more efficient reconstructions compared to the FWI method. We evaluate the performance of our approach on in-silico data and show that neglecting nonlinear effects may result in substantial degradation in the reconstruction, paving the way of NWI into clinical applications.

On stress in abdominal aortic aneurysm: Linear versus non-linear analysis and aneurysm rupture risk.

We present comprehensive biomechanical analyses of abdominal aortic aneurysms (AAA) for 43 patients. We compare stress magnitudes and stress distributions within arterial walls of abdominal aortic aneurysms (AAA) obtained using two simulation and modelling methods: (a) Fully automated and computationally very efficient linear method embedded in the software platform Biomechanics based Prediction of Aneurysm Rupture Risk (BioPARR), freely available from https://bioparr.mech.uwa.edu.au/; (b) More complex and much more computationally demanding Non-Linear Iterative Stress Analysis (Non-LISA) that uses a non-linear inverse iterative approach and strongly non-linear material model. Both methods predicted localised high stress zones with over 90% of AAA model volume fraction subjected to stress below 20% of the 99th percentile maximum principal stress. However, for the non-linear iterative method, the peak maximum principal stress (and 99th percentile maximum principal stress) was higher and the stress magnitude in the low stress area lower than for the automated linear method embedded in BioPARR. Differences between the stress distributions obtained using the two methods tended to be particularly pronounced in the areas where the AAA curvature was large. Performance of the selected characteristic features of the stress fields (we used 99th percentile maximum principal stress) obtained using BioPARR and Non-LISA in distinguishing between the AAAs that would rupture and remain intact was for practical purposes the same for both methods.

A COMPARISON OF RAINFALL ESTIMATION USING HIMAWARI-8 SATELLITE DATA IN DIFFERENT INDONESIAN TOPOGRAPHIES

The Himawari-8 satellite can be used to derive precipitation data for rainfall estimation. This study aims to test several methods for suchestimation employing the Himawari-8 satellite. The methods are compared in three regions with different topographies, namely Bukittinggi, Pontianak and Ambon. The rainfall estimation methods that are tested are auto estimator, IMSRA, non-linear relation and non-linear inversion approaches. Based on the determination of the statistical verification(RMSE, standard deviation and correlation coefficient) of the amount of rainfall, the best method in Bukittinggi and Pontianak was shown to be IMSRA, while for the Ambon region was the non-linear relations. The best methods from each research area were mapped using the Google Maps Application Programming Interface (API).

Incremental Nonlinear Fault-Tolerant Control of a Quadrotor With Complete Loss of Two Opposing Rotors

In order to further expand the flight envelope of quadrotors under actuator failures, we design a nonlinear sensor-based fault-tolerant controller to stabilize a quadrotor with failure of two opposing rotors in the high-speed flight condition (> 8m/s). The incremental nonlinear dynamic inversion (INDI) approach which excels in handling model uncertainties is adopted to compensate for the significant unknown aerodynamic effects. The internal dynamics of such an underactuated system have been analyzed, and subsequently stabilized by re-defining the control output. The proposed method can be generalized to control a quadrotor under single-rotor-failure and nominal conditions. For validation, flight tests have been carried out in a large-scale open jet wind tunnel. The position of a damaged quadrotor can be controlled in the presence of significant wind disturbances. A linear quadratic regulator (LQR) approach from the literature has been compared to demonstrate the advantages of the proposed nonlinear method in the windy and high-speed flight condition.

Discrete-time incremental backstepping controller for unmanned aircrafts subject to actuator constraints

In the study, a discrete-time incremental backstepping (DTIBS) controller is proposed for the aircrafts with unknown actuator dynamics. Taylor series and approximating discretization approach are used, and thus the second-order continuous-time nonlinear system is modified as a discrete-time nonlinear plant in which input is in an incremental form. The incremental control laws are designed by using the incremental nonlinear dynamic inversion (INDI) approach and time-delayed control (TDC) method incorporating the robust terms by applying a standard gradient-based adaption method and the chain-rule. The TDC is introduced to design the control law, and thus concrete prior knowledge of the control effectiveness matrix involving a few unknown aerodynamic coefficients is not required. Furthermore, the stable linear filters in the discrete-time form are designed to compensate for the filtered errors and actuator dynamics. A comparison of the numerical simulation results verifies that DTIBS with the robust terms can significantly improve tracking performance. Root mean square error of the whole tracking process (RMSEOTP) is defined to demonstrate the high tracking accuracy of the controller.

Evaluating the methods and influencing factors of satellite-derived estimates of NOX emissions at regional scale: A case study for Yangtze River Delta, China

The top-down estimation of NOX emissions and their influencing factors were evaluated based on the “synthetic” and real satellite observation methods at different spatial scales in eastern China. Using the “synthetic” NO2 vertical column densities (VCD) simulated from a hypothetical “true” emission inventory, the top-down estimates of NOX emissions for the Yangtze River Delta (YRD) region at 9 km resolution and the Southern Jiangsu City Cluster (SJC) at 3 km resolution were obtained using various inverse modeling approaches and the a priori emissions for January and July 2012. The normalized mean biases (NMBs) between the top-down and the hypothetical “true” emissions for all the cases were smaller than 6%, which indicates that both linear and nonlinear approaches could effectively constrain the total amount of emissions, with limited influence from spatial resolution, a priori emissions, and seasons. Larger differences for most cases were found for the normalized mean errors (NMEs), implying that the inverse modeling approach and other influencing factors played a more important role on the spatial distribution of the top-down estimates. Two NO2 VCD products from real satellite observation (Dutch OMI NO2 data product v2 (DOMINO v2) and Peking University OMI NO2 data product v2 (POMINO v2)) were then applied to emissions constraints. The NMEs between the top-down estimates derived from the two products were calculated at 182% and 99% for January and July, respectively, indicating the great importance of satellite observation in constraining emissions. With the nonlinear inverse modeling approach, the top-down estimates of NOX emissions based on POMINO v2 were 25%–60% smaller than the national bottom-up inventory for the four seasons in the YRD, which indicates overestimation by the bottom-up method due to the insufficient consideration of recent air pollution control policy. At the 9 km resolution, the simulated NO2 concentrations with air quality modeling based on the top-down estimates were much closer to available ground observation than the bottom-up ones for all seasons, which suggests improved emissions estimation from the inverse model at regional scales.

Seismic inversion for fluid bulk modulus based on elastic impedance

Beginning with the simplification of Gassmann's fluid substitution equation, we propose a simplified bulk modulus of saturated rock in terms of fluid bulk modulus and porosity. Using relationship between reflection coefficients and scattering function, we derive a linearized PP-wave reflection coefficient as a function of fluid bulk modulus and modified porosity, and we also present the corresponding elastic impedance, which is useful for modeling how fluids affect seismic reflection amplitudes. The accuracy of derived reflection coefficient is confirmed in the case of maximum incidence angle being around 30°. Using the derived reflection coefficient and EI, we establish an inversion approach to estimate fluid bulk modulus and porosity from observed seismic data, which involves 1) the estimation of EI from partially stack seismic data, and 2) the extraction of fluid bulk modulus from estimated EI datasets. The extraction of fluid bulk modulus is implemented using a nonlinear inversion approach. Using the derived elastic impedance we compute the gradient of energy residual with respect to model vector directly, which allows us to implement the nonlinear inversion stably. Synthetic tests confirm the stability and robustness of the proposed inversion approach, and applying the inversion approach to a real dataset we obtain meaning results of fluid bulk modulus that are valuable for fluid identification in reservoirs.

Outer trench slope flexure and faulting at Pacific basin subduction zones

SUMMARY Flexure and fracturing of the seafloor on the outer trench wall of subduction zones reflect bending of the lithosphere beyond its elastic limit. To investigate these inelastic processes, we have developed a full nonlinear inversion approach for estimating the bending moment, curvature and outer trench wall fracturing using shipboard bathymetry and satellite altimetry-derived gravity data as constraints. Bending moments and downward forces are imposed along curved trench axes and an iterative method is used to calculate the nonlinear response for 26 sites in the circum-Pacific region having seafloor age ranging from 15 to 148 Ma. We use standard thermal and yield strength envelope models to develop the nonlinear moment versus curvature relationship. Two coefficients of friction of 0.6 and 0.3 are considered and we find that the lower value provides a better overall fit to the data. The main result is that the lithosphere is nearly moment saturated at the trench axis. The effective elastic thickness of the plate on the outer trench slope is at least three times smaller than the elastic thickness of the plate before bending at the outer rise in agreement with previous studies. The average seafloor depth of the unbent plate in these 26 sites matches the Parsons &amp; Sclater depth versus age model beyond 120 Ma. We also use the model to predict the offsets of normal faults on the outer trench walls and compare this with the horst and graben structures observed by multibeam surveys. The model with the lower coefficient of friction fits the fault offset data close to the trench axis. However, the model predicts significant fracturing of the lithosphere between 75 and 150 km away from the trench axis where no fracturing is observed. To reconcile these observations, we impose a thermoelastic pre-stress in the lithosphere prior to subduction. This pre-stress delays the onset of fracturing in better agreement with the data.

Combining Homogeneous High Order Sliding Mode and Nonlinear Dynamic Inversion for fixed wing aircraft attitude and speed control

Abstract This paper addresses the problem of robust flight control for fixed wing aircrafts. Such systems are generally of Multi-Input Multi-Output (MIMO) form, tightly coupled and highly nonlinear whereby the nonlinearity resides both in the dynamic equations and in the aerodynamic coefficients. Consequently, we propose to combine Homogeneous High Order Sliding Mode (HHOSM) and Nonlinear Dynamic Inversion (NDI) approaches in order to deal with the piloting controller. The overall controller is designed so as to ensure the tracking of desired longitudinal velocity and attitude angles. The dynamics inversion uses nonlinear full-state feedback to globally linearize the dynamics of the selected controlled variables so that a linear controller can then be applied to regulate these variables with a desirable closed-loop behavior. To handle the nonlinearity, the desired closed-loop dynamics are given by an HHOSM controller. Simulations are carried out on a real-time virtual simulation platform for the development of Aircraft Control Systems (ACS). The obtained results demonstrate the effectiveness of the proposed controller. It is shown that HHOSM-NDI autopilot delivers a high dynamic tracking performance and can alleviate the chattering effect. Moreover, finite time convergence to the origin is ensured.

VTOL UAV Transition Maneuver Using Incremental Nonlinear Dynamic Inversion

The paper seeks to study the control system design of a novel unmanned aerial vehicle (UAV). The UAV is capable of vertical takeoff and landing (VTOL), transition flight and cruising via the technique of direct force control. The incremental nonlinear dynamic inversion (INDI) approach is adopted for the 6-DOF nonlinear and nonaffine control of the UAV. Based on the INDI control law, a method of two-layer cascaded optimal control allocation is proposed to handle the redundant and coupled control variables. For the weight selection in optimal control allocation, a dynamic weight strategy is proposed. This strategy can adjust the weight of the objective function according to the flight states and mission requirements, thus determining the optimizing direction and ensuring the rationality of the allocation results. Simulation results indicate that the UAV can track the target trajectory accurately and exhibit continuous maneuverability in transition flight.

Fast 3D multichannel deconvolution of electromagnetic induction loop-loop apparent conductivity data sets acquired at low induction numbers

Electromagnetic induction (EMI) sensors using sufficiently low-frequency harmonic sources and sufficiently small loop separations operate in the low-induction-number (LIN) domain for a relatively wide range of background conductivity. These systems are used in diverse near-surface investigations including applications from soil sciences, hydrology, and archaeology. The special case of portable multiconfiguration EMI sensors operating at frequencies [Formula: see text] offers the possibility of using a fast linear deconvolution method to interpret multichannel data sets in three dimensions. Here, we have developed a fast 3D inversion/deconvolution method regularized with 3D smoothness constraints and formulated in the hybrid spectral-spatial domain. Compared with other linear approaches, the spectral-spatial domain formulation significantly reduces the computational cost of the processing and opens the door for real-time 3D interpretation of large data sets consisting of more than 100,000 data points. First, we test our proposed algorithm on synthetic data sets computed with the full Maxwell theory. Then, we apply our method to a real four-configuration EMI data set acquired to map the thickness of peat layers embedded in a sandy environment. For the synthetic and the field example, we compared our result with the result obtained using a standard point-by-point 1D nonlinear inversion approach. This comparison demonstrates that the proposed methodology provides superior lateral resolution compared with the 1D nonlinear inversion, at the same time significantly reducing the computational cost of the processing.

Acoustic Waveform Inversion for Ocean Turbulence

AbstractThe seismic oceanography method is based on extracting and stacking the low-frequency acoustic energy scattered by the ocean heterogeneity. However, a good understanding on how this acoustic wavefield is affected by physical processes in the ocean is still lacking. In this work an acoustic waveform modeling and inversion method is developed and applied to both synthetic and real data. In the synthetic example, the temperature field is simulated as a homogeneous Gaussian isotropic random field with the Kolmogorov–Obukhov spectrum superimposed on a background stratified ocean structure. The presented full waveform inversion method is based on the ray-Born approximation. The synthetic seismograms computed using the ray-Born scattering method closely match the seismograms produced with a more computationally expensive finite-difference method. The efficient solution to the inverse problem is provided by the multiscale nonlinear inversion approach that is specifically stable with respect to noise. Full waveform inversion tests are performed using both the stationary and time-dependent sound speed models. These tests show that the method provides a reliable reconstruction of both the spatial sound speed variation and the theoretical spectrum due to fully developed turbulence. Finally, the inversion approach is applied to real seismic reflection data to determine the heterogeneous sound speed structure at the west Barents Sea continental margin in the northeast Atlantic. The obtained model illustrates in more detail the processes of diapycnal mixing near the continental slope.

Alternating first-arrival traveltime tomography and waveform inversion for near-surface imaging

Near-surface seismic imaging often plays a significant role in producing quality data processing results for the deep subsurface in land and shallow marine environments. First-arrival traveltime tomography is a common approach for near-surface imaging due to its high efficiency and simplicity. However, the method faces issues of missing hidden layers and resolving the structures with low resolution. On the other hand, waveform inversion should offer better solutions for dealing with these issues, but it may suffer from the cycle-skipping problem. We intend to use the advantages and reduce the disadvantages of the two methods by developing a new strategy of alternately applying traveltime tomography and waveform inversion through iterations. First-arrival traveltime tomography applies a wavefront raytracer and a nonlinear inversion approach. Waveform inversion is a multiscale approach in which a wavelet transform is applied in the data domain to better handle the cycle-skipping problem. By alternating the two inversions rather than performing a joint inversion, we reduce the memory requirements and avoid nonphysical scaling problems between the two approaches. Using one synthetic and two real data examples, we determine that alternating inversions minimize two separate objective functions at the same time and constrain the near-surface structures fairly well compared with the waveform inversion method alone. For the field examples, the new method avoids generating the obvious artifacts and provides results consistent with the geology analysis of those areas.

A nonlinear control approach for a hypersonic vehicle

PurposeThe purpose of the paper is to design a robust control system for a generic hypersonic vehicle which includes dynamic nonlinear, open loop unstable and parametric uncertainties.Design/methodology/approachFor a complex longitudinal model of a generic hypersonic vehicle which includes dynamic nonlinear, open loop unstable and parametric uncertainties, a nonlinear dynamic inverse (NDI) approach combined with proportional differential (PD) control is used to design a strong robust control system to deal with the sensitivity to changes of atmosphere condition. In this way, a simple genetic algorithm is used to search a group of parameters of the control system to satisfy the specific performance indices. Then parametric uncertainties are considered to verify the robustness of the control system.FindingsThe PD hypersonic vehicle control system using NDI approach can satisfy the specific flight performance. And it has strong robustness under the parametric uncertainties.Originality/valueThe paper fulfills a complete process of the nonlinear control system design for a generic hypersonic vehicle. And, the simulation results show the efficiency and robustness of the control system.