Inverse Error Research Articles

Weak Lensing Analysis of A2390 Using Short Exposures

We present a weak lensing analysis of the galaxy cluster A2390 at z = 0.23 using second moment shape measurements made in 411 short 60 s exposures. The exposures are obtained in three broadband photometric filters (g, r, and i) using WIYN-ODI. Shape measurement in individual exposures is done using a moment-matching algorithm. Forced measurement is used when the moment-matching algorithm fails to converge at low signal-to-noise ratio. The measurements made in individual images are combined using inverse error weighting to obtain accurate shapes for the sources and hence recover shear. We use PhoSim simulations to validate the shear measurements recovered by our pipeline. We find the mass of A2390 is in agreement with previously published results. We also find the E-mode maps show filamentary structures consistent with baryonic structures and recover most clusters/groups of galaxies found using optical and X-ray data. Thus, we demonstrate the feasibility of using weak lensing to map large-scale structure of the Universe. We also find the central portion of the cluster has a bimodal mass distribution and the relative orientation of the peaks is similar to X-ray. We discuss earlier research on this galaxy cluster, and show that a late-stage merger accounts for all the observed data.

Inverse Identification of Constituent Elastic Parameters of Ceramic Matrix Composites Based on Macro–Micro Combined Finite Element Model

Accurate material performance parameters are the prerequisite for conducting composite material structural analysis and design. However, the complex multiscale structure of ceramic matrix composites (CMCs) makes it extremely difficult to accurately obtain their mechanical performance parameters. To address this issue, a CMC micro-scale constituents (fiber bundles and matrix) elastic parameter inversion method was proposed based on the integration of macro–micro finite element models. This model was established based on the μCT scan data of a plain-woven CMC tensile specimen using the chemical vapor infiltration (CVI) process, which could reflect the real microstructure and surface morphology characteristics of the material. A BP neural network was used to predict the multiscale stiffness, considering the influence of the porous structure on the macroscopic stiffness of the material. The inversion process of the constituent elastic parameters was established using the trust-region algorithm combined with an improved error function. The inversion results showed that this method could accurately invert the CMC constituent elastic parameters with excellent robustness and anti-noise performance. Under four different degrees of deviation in the initial iteration conditions, the inversion error of all parameters was within 1%, and the maximum inversion error was only 2.16% under a 10% high noise level.

A Novel Axial Load Inversion Method for Rock Bolts Based on the Surface Strain of a Bearing Plate

Anchor rock bolts are among the essential support components employed in coal mine support engineering. Measuring the axial load of the supporting anchor bolts constitutes an important foundation for evaluating the support effect and the mechanical state of the surrounding rock. The existing methods for measuring the axial load of rock bolts have difficulty meeting the actual demands in terms of accuracy and means. Therefore, we propose a novel inverse method for determining the axial load of rock bolts. On the basis of the dynamic relationship between the axial load of the anchor bolt and the strain of the plate, a calculation model for the inverse analysis of the axial load from the plate strain is presented, and it is verified and corrected through finite element analysis and indoor physical experiments. By combining the calculation model with the digital image correlation method, a low costinversion of the axial load of the anchor bolt in actual support engineering is achieved. The experimental results demonstrate that the average errors of the load inversion of anchor bolts in three different states via the theory and method proposed in this paper are less than 8.8% (4 kN), 3.6% (3.2 kN), and 14.7% (5.5 kN), respectively, and the average error of the axial load of the rock bolts in the proposed method is only 4.23 kN. It possesses relatively high accuracy and can be effectively applied in the actual production processes of mines.

Improved Synchrosqueezing S-Transform and Its Application in Reinforcement Protection Layer Identification

Abstract Synchrosqueezing is a strategy to enhance the resolution of time-frequency analysis. However, its application in the S-transform leads to complexities due to the variable phase spectrum of the S-transform, resulting in a decrease in resolution and an increase in complexity. This work proposes an Synchrosqueezing Generalized S-Transform (SS-GPST) by introducing phase-shifting and a generalized parameter to simplify the mathematical definition and enhance resolution. Synthetic data trials demonstrate the superiority of SS-GPST over existing synchrosqueezing methods, offering enhanced resolution and minimized inverse transformation errors. In practical ground-penetrating radar applications, we have applied SS-GPST to identify the reinforcement protection layer in tunnel linings. The results show that SS-GPST offers a novel method for thin-layer extraction in ground-penetrating radar applications.

A study on hybrid light extinction model and inversion based on Lambert-Beer Law

A hybrid light extinction model (LEM) applicable only to spherical particles has been proposed, in which the extinction cross-section weighted by mixing ratio and particle size distribution was introduced to study the light extinction characteristics of polydisperse mixed particles. Moreover, an extinction spectra measurement system has been established, and a series of experiments were performed for mixed particles of silica and polystyrene particles, with mixing ratios of 0.25, 0.5, and 0.75. The results show that the hybrid light extinction method calculations agree well with the experimental spectra, with root mean square errors within 0.07. Subsequently, a differential evolutionary algorithm has been investigated to achieve simultaneous multi-parameter inversion of the polydisperse mixed particles under different mixing ratios. The inversion results show that the error for any single parameter is < 7.89%. It is worth noting that the LEM is extended to six-parameter measurements, including particle size distribution, mixing ratio, and number concentration. The maximum inversion errors for particle size, mixing ratio, and number concentration are observed at 9.28%, 2.63%, and 16.90%. Furthermore, the resultant distribution parameters also precisely reflected the narrow particle size distribution of the experimental samples, as confirmed by SEM results.

Evaluation of satellite-derived precipitation datasets: a case study in the Ten Tributaries region of the Yellow River Basin

ABSTRACT Satellite-derived precipitation datasets are essential components of hydrological simulations, particularly in data-scarce regions of western China. However, a comprehensive assessment of their accuracy and reliability is required. Here, the accuracy of two high-resolution satellite-derived precipitation datasets, Integrated Multi-satellite Retrievals for GPM – Final (IMERG-F) and Gauge-Adjusted Global Satellite Mapping of Precipitation (GSMaP-Gauge), was evaluated across the Ten Tributaries region of the Yellow River Basin in western China using four quantitative metrics and three categorical scoring indicators. This evaluation sought to ascertain the retrieval accuracy of these products on both the daily scale and hourly scale of heavy precipitation events, and investigated their inversion error characteristics across various spatiotemporal scales. Both datasets effectively captured the spatiotemporal patterns of annual average precipitation within the study area. Notably, the daily-scale accuracy of these satellite-derived precipitation products surpassed their hourly and half-hourly counterparts. Both GPM-IMERG and GSMaP-Gauge adeptly reproduced most precipitation events in the Ten Tributaries region, with peak detection performance observed in the central and southern zones, providing a reliable data source for drought monitoring and hydrological modeling. Overall, compared with GPM-IMERG, GSMaP-Gauge displayed superior inversion accuracy across diverse spatiotemporal scales.

Study and Analysis of the Thunder Source Location Error Based on Acoustic Ray-Tracing

Error analysis and estimation of thunder source location results is a prerequisite for obtaining accurate location results of thunder sources, which is of great significance for a deeper understanding of the physical process of lightning channel discharges. Most of the thunder source location algorithms are based on the simplified model of the straight-line propagation of acoustic waves to determine the location of the thunder source; however, the acoustic wave is affected by the inhomogeneity of the atmosphere medium in the propagation process and its acoustic ray will be bent. Temperature and humidity are the main factors affecting the vertical distribution of the velocity of sound in the atmosphere, therefore, it is necessary to study the changes in location errors under the models of uniform vertical distribution of temperature only and uniform vertical distribution of humidity only. This paper focuses on the theory of acoustic ray-tracing in neglecting the presence of the wind and the acoustic attenuation and the theoretical derivation of the location error of thunder source inversion for the three models is carried out by using MATLAB R2019b programming. Then, simulation analysis and comparative study on the variation law of thunder source location error with the height of the source, ground temperature, ground humidity, and array position under the three models are carried out. The results of the study show that the maximum location error can be obtained from the straight-line propagation model, the location error obtained from the model of uniform vertical distribution of temperature only is the second, and the location error obtained from the model of uniform vertical distribution of humidity only is the least and can be negligible compared to the first two models. In the trend of error variation, the variation of location error with temperature and humidity is relatively flat in the first two models; however, the variation of location error with the height of the thunder source is more drastic, which can be more than 80%. The location error obtained from the array inversion closer to the thunder source increases linearly with the height of the thunder source, the location error obtained from the more distant array inversion shows a fast-decreasing trend at the height of the thunder source from 500 to 3500 m, and a flat trend above 3500 m. The location error varies relatively smoothly with the height of the thunder source, the ground temperature, and the ground humidity in the model of uniform vertical distribution of humidity only. In addition, the position of the array also has an important effect on lightning location. The further the horizontal distance from the source, the greater the location error will be obtained in the first two models, and when the thunder source is at a low height and detected at a long distance, the location error will be very large, so relevant data should be modified in actual observation.

Optical parameter inversion of thin films based on angular reflectance spectroscopy

This article proposes a method for obtaining the refractive index and thickness of thin films based on reflectivity at different angles combined with optimization algorithms. This method has high computational accuracy for both high absorption films (such as aluminum films, gold films, etc.) and low absorption films (such as MgF2 films). Since this study did not adopt the inversion scheme of refractive index dispersion equation fitting, it can be used for optical constant inversion in the case of unknown composition of coating materials. The results indicate that this method can simultaneously obtain high-precision information on the complex refractive index and film thickness of the coating material on the substrate. The calculation example achieved a thickness inversion error of 0.165 % for a 2nm metal aluminum film layer and 0.3303 % for a 150 nm MgF2 transparent film layer. Therefore, this study may provide further guidance for high absorption and measurement of the complex refractive index and thickness of transparent films.

Research on Digital Twin Method for Spaceborne Along-Track Interferometric Synthetic Aperture Radar Velocity Inversion of Ocean Surface Currents

In this paper, an end-to-end system framework is proposed for the Digital Twin study of spaceborne ATI-SAR ocean current velocity inversion. Within this framework, a fitting inversion approach is proposed to enhance the conventional spaceborne ATI-SAR ocean current velocity inversion algorithm. Consequently, the issue of possible local inversion errors stemming from the mismatch between the traditional spaceborne ATI-SAR inversion algorithm and various dual-antenna configurations is resolved to a certain extent. A simulated spaceborne ATI-SAR system, featuring a dual-antenna configuration comprising a baseline direction perpendicular to the track and a squint angle, is presented to validate the efficacy of the Digital Twin methodology. Under the specified simulation parameters, the average inversion error for the final ocean current velocity is recorded at 0.0084 m/s, showcasing a reduction of 0.0401 m/s compared with the average inversion error prior to optimization.

Extended Monte Carlo modeling for submicron particle size measurement under high light extinction conditions.

The light extinction method (LEM) based on Lambert Beer's law (LB) is widely used to characterize particle size distribution (PSD) in multiphase flow. However, as the optical thickness increases with concentration, the phenomenon of multiple scattering is enhanced, potentially leading to reduced accuracy and a limited application range. In this study, an extended Monte Carlo-based light extinction model (EMC) was developed, which was initially employed to calculate and evaluate the impact of multiple scattering. Subsequently, it was used to predict the extinction spectrum that incorporates multiple scattering effects under varying concentrations. To validate the modeling, a compact setup was constructed to perform a series of experiments on polystyrene and silica dioxide (SiO2) suspensions. A differential evolution algorithm was also implemented for the inversion of PSD based on spectral content, with the incorporation of an improved coefficient matrix that considers multiple scattering effects. In comparison to the linear LB model, the EMC exhibits a markedly enhanced capacity in handling higher particle concentrations and improving measurement accuracy. For a 700 nm PS suspension, the particle size inversion error of the EMC can be kept within 4% (93.86% for the LB model) compared with the nominal value, even with an optical thickness of 5.

An example of the application of neural networks of a simple architecture to unfocused well electrometry probes

An effective method of finding stable solutions of inverse problems of electric and induction logging along the well is proposed, which allows avoiding the influence of the resistance values of the neighboring formations on the determination of the geoelectrical parameters of the object under study. A highly efficient method was proposed for solving such an unstable inverse problem. This method is based on the application of a neural network with inverse error propagation of a simple architecture. Namely three-layer. The mathematical statement of the problem is given, both the topology of the neural network and all its parameters are described in detail. In the course of the numerical experiment, they were selected as optimal. The process of building a base for training a neural network is described in detail. Namely, how each of the examples of the learning base is built by solving a direct problem. With this cut parameter, the training for each example is chosen arbitrarily, which guarantees a comprehensive range for training the neural network. The number of examples in the training base is one hundred thousand examples. As the activation function, the sigmoid is chosen due to the fact that it is differentiable everywhere. The results of testing the written program are given. The learning rate was estimated to obtain the required small error. It is shown that this approach is stably convergent. For testing, the parameters of the layers of the cut, which are inherent to the geophysical parameters of the cuts of the Dnipro-Donetsk depression, were chosen. A complex of lateral logging sounding was chosen as the electrical logging equipment. Four-probe low-frequency induction logging equipment was chosen as induction logging equipment. Examples for induction and electrical logging are given separately. The obtained results are analyzed in detail. Ways of further improvement of the obtained neural network and its use for other problems of geophysics are given.

Inversion-based fuzzy adaptive control with prespecifiable tracking accuracy for uncertain hysteretic systems

Inversion-based control strategies have the outstanding effectiveness in the compensation for hysteresis nonlinearities. However, when the plant is driven by smart material-based actuator with the information absence of hysteresis output, there still exist technical gaps in the construction of hysteresis inverse controller. Therefore, this study aims to address this gap by proposing a novel control scheme. Technically, a novel hysteresis inverse algorithm, significantly reducing computational burden, has been proposed based on a novel adaptive estimation method for the unknown parameter (density function) in the Preisach-typed hysteresis nonlinearity. Furthermore, the inverse compensation error, the nonlinearities and uncertainties appeared in the controlled plant are accommodated by the innovative adaptive fuzzy feedback controller. With our scheme, it can ensure that the closed-loop stability, predefined steady-stated tracking performance and the convergence of algorithms including inverse algorithm and adaptive updating laws. In addition to theoretical analysis, we have validated the effectiveness of the proposed control scheme through simulation comparisons and experimental results conducted by the real-life piezoelectric actuator.

Modeling of dynamic characteristics and μ-synthesis control of piezoelectric positioning platform

Abstract The dynamic hysteresis nonlinearity and various uncertainties of the piezoelectric positioning platform are critical factors limiting its high-precision applications. To address this, the dynamic characteristics of the piezoelectric positioning platform under various loads are identified based on the linearization of the Prandtl-Ishlinskii inverse model. The inverse compensation error and load disturbances are attributed to model uncertainties, which are modeled in the frequency domain. A μ-synthesis controller is designed to improve the tracking accuracy of the piezoelectric positioning platform under uncertainty disturbances. Experimental results indicate that with the μ-synthesis controller, the piezoelectric positioning platform achieves a relative error (RE) of less than 2.71% when unloaded. The RE is less than 6.03% for load disturbances of 100g, 200g, and 300g, respectively. These results demonstrate that the designed controller meets the high-precision positioning performance requirements under various load disturbance conditions.

Research on Fourier Coefficient-Based Energy Capture for Direct-Drive Wave Energy Generation System Based on Position Sensorless Disturbance Suppression

In order to improve the energy capture efficiency of direct-drive wave power generation (DDWEG) systems and enhance the robustness of the reference power tracking control, a Fourier coefficient-based energy capture (FCBEC) and a position sensorless disturbance suppression (PSDS) control strategy are proposed. For energy capture, FCBEC is proposed to construct the objective function by maximizing the average power over a period of time and expanding the variables in the Fourier basis when the maximum power is captured, which is used as the basis for obtaining the reference trajectory. To address the limitations of the mechanical encoder, the position sensorless technique, based on a sliding mode observer (SMO), is used in the power tracking control, and the position information is obtained through an inverse tangent function. The perturbation caused by the inverse electromotive force error in the system is theoretically analyzed. A full-order terminal sliding mode approach is employed to design a current controller that suppresses the perturbation and ensures accurate tracking of the reference current. Simulation results show that the ocean-wave energy capture strategy proposed in this paper can make the energy captured by the PTO reach the optimal value under the impedance matching condition, and that the response speed and robustness of the full-order terminal sliding mode are better than the traditional PI control.

Adaptive Sliding Mode Trajectory Tracking Control of Unmanned Surface Vessels Based on Time-Domain Wave Inversion

In this work, we develop a trajectory tracking control method for unmanned surface vessels (USVs) based on real-time compensation for actual wave disturbances. Firstly, wave information from the actual sea surface is extracted through stereoscopic visual observations, and data preprocessing is performed using a task-driven point cloud downsampling network. We reconstruct the phase-resolved wave field in real time. Subsequently, the wave disturbances are modeled mechanically, and real-time wave disturbances are used as feedforward inputs. Furthermore, an adaptive backstepping sliding mode control law based on command filters is designed to avoid differential explosion and mitigate sliding mode chattering. An adaptive law is also designed to estimate and compensate for other external disturbances and inversion error bounds that cannot be computed in real time. Finally, the feasibility of the proposed control strategy is validated through stability analysis and numerical simulation experiments.

Transient electromagnetic inversion to image the shallow subsurface based on convolutional bidirectional long short-term memory neural networks

SUMMARY The conventional transient electromagnetic inversion method has a low calculation speed and precision and is susceptible to falling into local minima, which does not meet the fine detection requirements of urban underground space. In this study, we proposed a novel inversion method based on convolutional bidirectional long short-term memory neural networks for shallow subsurface transient electromagnetic inversion. This network structure possessed strong spatial feature extraction capabilities and a proficient understanding of sequential data, thereby addressing the issues of slow conventional inversion computations and inadequate inversion accuracy. Utilizing the apparent resistivity from a three-layer model as the sample input and the real model as the target, the network was trained using batch normalization and dropout techniques to accelerate the convergence rate. The resulting model achieved real-time inversion speeds and high accuracy, with robust generalization capabilities and adaptability to new data. To assess the inversion performance, we used a novel 1-D inversion error calculation index, the correlation area loss error, for a more accurate measurement. Numerical simulation experiments showed that the proposed method required only 2.121 s to invert data from 100 observation points. The inversion efficiency was significantly superior to the conventional methods, maintaining excellent accuracy while effectively discerning subsurface electrical stratification in geophysics. Applying convolutional bidirectional long short-term memory neural networks to multidimensional and field data yielded results superior to those of conventional inversion, demonstrating the promising applicability and generalization of this approach. This study offers an efficient solution for shallow subsurface transient electromagnetic exploration and holds potential for application in other areas.

Study on Optimization Method for InSAR Baseline Considering Changes in Vegetation Coverage.

Time-series Interferometric Synthetic Aperture Radar (InSAR) technology, renowned for its high-precision, wide coverage, and all-weather capabilities, has become an essential tool for Earth observation. However, the quality of the interferometric baseline network significantly influences the monitoring accuracy of InSAR technology. Therefore, optimizing the interferometric baseline is crucial for enhancing InSAR's monitoring accuracy. Surface vegetation changes can disrupt the coherence between SAR images, introducing incoherent noise into interferograms and reducing InSAR's monitoring accuracy. To address this issue, we propose and validate an optimization method for the InSAR baseline that considers changes in vegetation coverage (OM-InSAR-BCCVC) in the Yuanmou dry-hot valley. Initially, based on the imaging times of SAR image pairs, we categorize all interferometric image pairs into those captured during months of high vegetation coverage and those from months of low vegetation coverage. We then remove the image pairs with coherence coefficients below the category average. Using the Small Baseline Subset InSAR (SBAS-InSAR) technique, we retrieve surface deformation information in the Yuanmou dry-hot valley. Landslide identification is subsequently verified using optical remote sensing images. The results show that significant seasonal changes in vegetation coverage in the Yuanmou dry-hot valley lead to noticeable seasonal variations in InSAR coherence, with the lowest coherence in July, August, and September, and the highest in January, February, and December. The average coherence threshold method is limited in this context, resulting in discontinuities in the interferometric baseline network. Compared with methods without baseline optimization, the interferometric map ratio improved by 17.5% overall after applying the OM-InSAR-BCCVC method, and the overall inversion error RMSE decreased by 0.5 rad. From January 2021 to May 2023, the radar line of sight (LOS) surface deformation rate in the Yuanmou dry-hot valley, obtained after atmospheric correction by GACOS, baseline optimization, and geometric distortion region masking, ranged from -73.87 mm/year to 127.35 mm/year. We identified fifteen landslides and potential landslide sites, primarily located in the northern part of the Yuanmou dry-hot valley, with maximum subsidence exceeding 100 mm at two notable points. The OM-InSAR-BCCVC method effectively reduces incoherent noise caused by vegetation coverage changes, thereby improving the monitoring accuracy of InSAR.

Inversion of extinction coefficient for scattering media based on range-gated detection.

The extinction coefficient is an important parameter for describing light transmitting properties in the scattering medium. However, the single-point detection way and the large inversion error of the existing techniques cannot satisfy the need for spatial analysis and data application. A novel approach for inversion of extinction coefficient based on range-gated detection utilizing backward scattering of medium is proposed, and an inversion algorithm for extinction coefficient is established utilizing the backscattering signal of multiple adjacent spatial slices of the medium. The method can simultaneously invert transverse multiple-points extinction coefficient and longitudinal profile of extinction coefficient. Further, experiments are conducted in the scattering medium including fog and smoke based on the fabricated range-gated extinction-coefficient detection and inversion system, and the results demonstrate that inversion with the error less than 5% can be achieved at different detection distances, different concentrations and different kinds of scattering mediums. This approach offers a convenient, rapid and accurate means to acquire extinction coefficients, laying the foundation for the development of efficient environmental monitoring and high-quality defogging imaging.

Experimental investigation of pore-filling substitution effect on frequency-dependent elastic moduli of Berea sandstone

SUMMARY Based on both forced oscillation and ultrasonic pulse transmission methods, we investigated solid pore infill influences on rock elastic moduli in a broad frequency range $[ {1 - 3000,\,\,{{10}^6}} ]$ Hz for different differential pressures. For a Berea sandstone sample, filled sequentially by solid (${22\,\,^{\rm{o}}}{\rm{C}}$), quasi-solid (${26\,\,^{\rm{o}}}{\rm{C}}$) and liquid (${34\,\,^{\rm{o}}}{\rm{C}}$) octadecane, a frequency-dependence was found for the Poisson's ratio, Young's modulus and bulk modulus, nevertheless, these elastic parameters were strongly suppressed by increasing pressures. Experimental measurements showed that shear wave velocity and modulus of solid-octadecane-filled samples are significantly larger than those of the dry and liquid-octadecane-filled ones, implying the potential stiffening effects related to solid infill in compliant pores. A three porosity structure model, which describes the solid stiffening effects related to equant, compliant and the intermediate pores with aspect ratios larger than those of compliant pores but much less than those of stiff pores, was used to compare against the experimentally measured elastic properties for octadecane pore infill, together with several other fluid/solid substitution theories. The agreement between experimental measurements and theoretical predictions is reasonably good for the sandstone tested, providing that the three porosity model can be applied for pressure- and frequency-dependent elastic moduli estimations for a viscoelastic pore-infill-saturated sandstone. Evaluating the combined squirt flow mechanism responsible for the observed moduli dispersion and attenuation is of great importance to reduce potential errors in seismic AVO inversion and 4-D seismic monitoring of gas-hydrate or bitumen-saturated reservoir, especially for reservoir rocks with complex microstructures and heterogeneous pore types.

A Novel Localized Fast Multipole Method for Computations With Spatially Correlated Observation Error Statistics in Data Assimilation

AbstractSeveral observation types (e.g., geostationary satellite and Doppler radar observations) have recently been found to exhibit strong spatial error correlations. Including these error statistics in data assimilation for numerical weather prediction can improve analysis quality and forecast skill. Moreover, it allows for increases in the spatial density of observations assimilated, which is needed for the provision of information on appropriate scales for high‐resolution forecasting. However, introducing correlated error statistics may increase the computational complexity and parallel communication costs of matrix‐vector products involving observation precision matrices (inverse observation error covariance matrices). Without new approaches, we cannot take full advantage of new observation uncertainty estimates. We develop a new numerical approximation method based on a particular type of fast multipole method and a domain localization approach. The basic idea is to divide the observation domain into boxes and then separate calculations of matrix‐vector products according to the partition. These calculations can be done in parallel with very low communication overheads. The new method is easy to implement and parallelize, and it is applicable to a wide variety of observation precision matrices. We applied the new method to a simple variational data assimilation problem and found that the computational cost of the variational minimization was dramatically reduced while preserving analysis accuracy across a range of scales. The new method has the potential to be used as an efficient technique for practical applications where a large number of observations with mutual error correlations need to be assimilated quickly.