Inversion Algorithm Research Articles

NaNDC: Full Moment Tensor Inversion and Uncertainty Analysis for Large-N Monitored Small Earthquakes

Abstract Although most earthquakes occur on near-linear planes and generate shear motions, the small-moderate events may contain explosive or nonlinear features, translating into the “non-double-couple” (NDC) components in the full moment tensors (FMTs). However, constraining such secondary components remains challenging and often involves full-waveform-based modeling, demanding high-resolution 3D velocity structures that are barely available at local scales. Alternatively, the recent boost of the dense nodal array provides an opportunity to resolve FMTs using polarities and amplitudes of body waves. In this study, we propose an FMT inversion algorithm that joints different far-field observations (i.e., P-wave polarities and amplitudes, S/P amplitude ratios) to constrain the NDC components for small earthquakes monitored by nodal arrays (nodal array non-double couple [NaNDC]). The optimal moment tensor and associated uncertainties are determined through a grid search over FMT space. Then uncertainties of the NDC components are projected onto the Lune plot for illustration. Synthetic tests demonstrate the robustness and high tolerance of NaNDC for station coverage, noise level, and perturbed velocity models, as well as the case-dependent benefit of incorporating S/P amplitude ratios in constraining FMTs. We then applied NaNDC to field observations near a hydraulic-fracturing well in Western Canada, where 167 M > 1 induced events were recorded by 69 three-component geophones. The resolved FMTs are predominantly strike-slip with subvertical or shallow dip nodal planes, with an average percentage of the double-couple component greater than 70%. Although our solutions are generally consistent with the previous results (90% of events displayed angular difference less than 20°), NaNDC reduced the amounts of NDC components for events located to the northeast. We provide NaNDC as an effective tool for FMT inversion of large-N-monitored small earthquakes. The uncertainty evaluation on the Lune plot also permits a more precise and quantitative interpretation of the NDC components observed from complex environments like volcanic or induced regions.

Mechanically anisotropic phantoms for magnetic resonance elastography.

Imaging phantoms with known anisotropic mechanical properties are needed to evaluate magnetic resonance elastography (MRE) methods to estimate anisotropic parameters. The aims of this study were to fabricate mechanically anisotropic MRE phantoms, characterize their mechanical behavior by direct testing, then assess the accuracy of MRE estimates of anisotropic properties using a transversely isotropic nonlinear inversion (TI-NLI) algorithm. Directionally scaled and unscaled lattices were designed to exhibit anisotropic or isotropic mechanical properties. Lattices were three-dimensionally printed in poly(ethelyne glycol) diacrylate using a commercial digital light processing printer, then infilled with gelatin to form a composite material. Benchtop testing determined two shear stiffnesses, and , governing loading parallel and perpendicular to the symmetry axis, and two analogous Young's moduli and . From these measures, shear anisotropy = and tensile anisotropy = were calculated. Three phantoms were driven by a central actuator and imaged with MRE at frequencies from 300 to 500 Hz. From MRE data, the TI-NLI algorithm estimated maps of , , and . In benchtop tests, geometrically scaled lattice composites exhibited the following anisotropic properties: = 6.1 ± 0.7 kPa, = 0.83 ± 0.13, = 0.78 ± 0.09} (mean ± standard deviation). MRE of scaled lattice composites revealed elliptical wavefields; TI-NLI analysis identified the following median property ranges: = 11-19 kPa, = 0.6-1.0, = 0.8-1.6}. Anisotropic MRE phantoms are created by embedding anisotropic three-dimensionally printed lattices into a softer matrix. The TI-NLI algorithm accurately estimates spatial contrast in anisotropic properties.

Network structure and fluctuation data improve inference of metabolic interaction strengths with the inverse Jacobian

Based on high-throughput metabolomics data, the recently introduced inverse differential Jacobian algorithm can infer regulatory factors and molecular causality within metabolic networks close to steady-state. However, these studies assumed perturbations acting independently on each metabolite, corresponding to metabolic system fluctuations. In contrast, emerging evidence puts forward internal network fluctuations, particularly from gene expression fluctuations, leading to correlated perturbations on metabolites. Here, we propose a novel approach that exploits these correlations to quantify relevant metabolic interactions. By integrating enzyme-related fluctuations in the construction of an appropriate fluctuation matrix, we are able to exploit the underlying reaction network structure for the inverse Jacobian algorithm. We applied this approach to a model-based artificial dataset for validation, and to an experimental breast cancer dataset with two different cell lines. By highlighting metabolic interactions with significantly changed interaction strengths, the inverse Jacobian approach identified critical dynamic regulation points which are confirming previous breast cancer studies.

Nitrogen monitoring and inversion algorithms of fruit trees based on spectral remote sensing: a deep review

Nitrogen monitoring and inversion algorithms of fruit trees based on spectral remote sensing: a deep review

Abel transform of laser-induced plasma image: Overcoming challenges of noisy and insufficient data for reliable reconstruction

Reconstructing spatial distribution of emissivity is important for study of heterogeneous plasma sources. However, often used Radon and Abel transforms tend to amplify noise in the data. The small size and short lifetime of laser-induced plasma result in short exposures for signal acquisition, and, consequently limited number of points along the source available for measurements and noisy signals. We compared 14 Abel transform algorithms and various noise processing methods, focusing on both limited data points and high noise levels. All algorithms were presented in matrix form to ensure fair comparison, and we proposed a metric based on the largest singular value of matrix operator for error assessment. An error analysis is performed to show the contribution of approximation and noise errors to the overall reconstruction error. Our results indicate that at higher noise levels, the choice of noise reduction method is more critical than the inversion algorithm itself, with regularization proving to be the most effective for noise control. Given the minimal impact of algorithm choice on the final result, simple and easy-to-implement methods like “Onion Peeling” are recommended to be combined with regularization. Furthermore, transforms with regularization were the most stable for reconstructing complex profiles. Summarizing the results for all considered cases, “Hankel-Fourier” and “Cubic Spline” are the most accurate for noiseless data with limited number of spatial points, while for cases with a large amount of data, “Polynomial”, “Piessens-Verbaeten”, and “Minerbo-Levy” are better, especially for noisy data.

Computational Design of a Kit of Parts for Bending Active Structures

Bending-active structures are composed of elastic elements that deform to achieve a desired target shape. To support effective design, inverse algorithms have been proposed that optimize the geometry of each element specifically for each design. This makes it difficult to reuse elements across designs or gain efficiency in fabrication through mass production. We address this issue and propose a computational framework to rationalize bending-active structures into a sparse kit of parts. Our method solves for the optimal part geometry such that multiple input designs can be faithfully realized with the same kit of parts. Assigning parts to different assemblies leads to a combinatorial explosion that makes exhaustive search intractable. Instead, we propose a relaxed continuous optimization incorporating a physics-based simulation in its inner loop to model the elastic deformation of the bending-active structure accurately. Our algorithm allows analyzing different design trade-offs of a kit of parts to tune the balance between fabrication complexity and fidelity to the original designs. We demonstrate our method on three different classes of bending-active structures, showcasing the effectiveness of our approach for part reuse and sustainable practices in fabrication-driven design.

TensCERs: Tension-Constrained Elastic Rods

We study ensembles of elastic rods that are tensioned by a small set of inextensible cables. The cables induce forces that deform the initially straight, but flexible rods into 3D space curves at equilibrium. Rods can be open or closed, knotted, and arranged in arbitrary topologies. We specifically focus on equilibrium states with no contacts among rods. Our setup can thus be seen as a generalization of classical tensegrities that are composed of rigid rods and tensile cables, to also support rods that elastically deform. We show how this generalization leads to a rich design space, where complex target shapes can be achieved with a small set of elastic rods. To explore this space, we present an inverse design optimization algorithm that solves for the length and placement of cables such that the equilibrium state of the rod network best approximates a given set of input curves. We introduce appropriate sparsity terms to minimize the number of required cables, which significantly simplifies fabrication. Using our algorithm, we explore new classes of bending-active 3D structures, including elastic tensegrity knots that only require a few internal cables. We design and fabricate several physical models from basic materials that attain complex 3D shapes with unique structural properties.

Active learning with human heuristics: an algorithm robust to labeling bias.

Active learning enables prediction models to achieve better performance faster by adaptively querying an oracle for the labels of data points. Sometimes the oracle is a human, for example when a medical diagnosis is provided by a doctor. According to the behavioral sciences, people, because they employ heuristics, might sometimes exhibit biases in labeling. How does modeling the oracle as a human heuristic affect the performance of active learning algorithms? If there is a drop in performance, can one design active learning algorithms robust to labeling bias? The present article provides answers. We investigate two established human heuristics (fast-and-frugal tree, tallying model) combined with four active learning algorithms (entropy sampling, multi-view learning, conventional information density, and, our proposal, inverse information density) and three standard classifiers (logistic regression, random forests, support vector machines), and apply their combinations to 15 datasets where people routinely provide labels, such as health and other domains like marketing and transportation. There are two main results. First, we show that if a heuristic provides labels, the performance of active learning algorithms significantly drops, sometimes below random. Hence, it is key to design active learning algorithms that are robust to labeling bias. Our second contribution is to provide such a robust algorithm. The proposed inverse information density algorithm, which is inspired by human psychology, achieves an overall improvement of 87% over the best of the other algorithms. In conclusion, designing and benchmarking active learning algorithms can benefit from incorporating the modeling of human heuristics.

A hybrid speed optimization strategy based coordinated scheduling between AGVs and yard cranes in U-shaped container terminal

In automated container terminals, the uninterrupted operation of the yard crane is crucial to guarantee the working efficiency of the terminal. The interaction efficiency between Automated Guided Vehicles (AGVs) and Yard Cranes (YCs) significantly impacts overall operational effectiveness. In this paper, coordinated scheduling between AGVs and YCs within a U-shaped container terminal is analyzed. A hybrid speed optimization strategy is suggested for AGVs to reduce energy consumption. It combines stage and continuous speed optimization methods. The continuous strategy is used for urgent tasks, optimizing completion time at a higher energy cost. For less time-sensitive tasks, the stage strategy reduces completion time while balancing energy consumption. Subsequently, a mixed-integer time-energy coordinated scheduling model is developed to minimize both the maximum completion time and energy. A chaotic Inverse Learning-based Slime-Mold Genetic Algorithm (LSMAGA) is proposed that utilizes PWLCM mapping and inverse learning for population initialization, combined with a genetic algorithm. This approach is designed to optimize the task configurations of AGVs and YCs, while also addressing the AGV speed optimization strategy. The effectiveness and advantages of the proposed algorithm are validated through a series of small-scale task experiments. Compared to other algorithms, the proposed algorithm demonstrates excellent convergence speed. Large-scale task experiments involving 200–3000 tasks further confirm the effectiveness of the hybrid strategy. This approach reduces the maximum completion time by an average of 8.21% and 11.45%, respectively, with only a minor increase in energy consumption. Also the maximum completion time of the stage speed strategy in this paper is reduced by 15.51% on average compared to other speed strategies. This enhancement significantly boosts the operation efficiency of the container terminal. Additionally, the impact of the AGV speed change strategy on energy consumption time during co-scheduling is investigated.

Polarisation Synthesis Applied to 3D Polarimetric Imaging for Enhanced Buried Object Detection and Identification

Detecting sub-surface objects poses significant challenges, partly due to attenuation of the ground medium and cluttered environments. The acquisition polarisation and antenna orientation can also yield significant variation of detection performance. These challenges can be mitigated by developing more versatile systems and algorithms to enhance detection and identification. In this study, a novel application of a 3D SAR inverse algorithm and polarisation synthesis was applied to ultra-wideband polarimetric data of buried objects. The principle of polarisation synthesis facilitates an adaptable technique which can be used to match the target’s polarisation characteristics, and the application of this revealed hidden structures, enhanced detection, and increased received power when compared to single polarisation results. This study emphasises the significance of polarimetry in ground-penetrating radar (GPR), particularly for target discrimination in high-lift-off applications. The findings offer valuable insights that could drive future research and enhance the performance of these sensing systems.

Frequency-dependent nonlinear AVO inversion for fluid mobility in viscoelastic media

Reservoir fluid mobility is defined as the ratio of rock permeability to fluid viscosity, which is an important attribute to guide the prediction of high-quality oil and gas reservoirs. Frequency-dependent amplitude variation with offset (AVO) inversion, based on viscoelastic theory, is a useful tool for fluid identification. In conventional pre-stack inversion, linear approximations are usually used to calculate the reflection coefficients, while nonlinear inversions are only occasionally carried out. However, the nonlinear equation for the reflection coefficient, derived from the exact Zoeppritz equation, has higher accuracy and fewer assumptions than the linear approximations. Therefore, we derive a nonlinear frequency-dependent reflection coefficient equation of the PP-wave in terms of P-wave velocity reflectivity, S-wave velocity reflectivity and fluid mobility, based on the relationship among fluid mobility, incident angle, and seismic wave frequency. We consider viscoelastic media and frequency-dependent responses to improve the authenticity of the reflection coefficients. Additionally, we develop a split-step inversion method for fluid mobility based on the Artificial Neural Network Inversion (ANNI) algorithm. Synthetic and field data examples demonstrate that the proposed split-step inversion method outperforms traditional inversion methods that rely on approximate equations for predicting underground reservoirs, improving the stability of fluid mobility parameter inversion.

IShapEditing: Intelligent Shape Editing with Diffusion Models

AbstractRecent advancements in generative models have enabled image editing very effective with impressive results. By extending this progress to 3D geometry models, we introduce iShapEditing, a novel framework for 3D shape editing which is applicable to both generated and real shapes. Users manipulate shapes by dragging handle points to corresponding targets, offering an intuitive and intelligent editing interface. Leveraging the Triplane Diffusion model and robust intermediate feature correspondence, our framework utilizes classifier guidance to adjust noise representations during sampling process, ensuring alignment with user expectations while preserving plausibility. For real shapes, we employ shape predictions at each time step alongside a DDPM‐based inversion algorithm to derive their latent codes, facilitating seamless editing. iShapEditing provides effective and intelligent control over shapes without the need for additional model training or fine‐tuning. Experimental examples demonstrate the effectiveness and superiority of our method in terms of editing accuracy and plausibility.

Enhancing computational efficiency in topology-optimized mode converters via dynamic update rate strategies

In the big data era, mode division multiplexing, as a technology for extended channel capacity, demonstrates potential in enhancing parallel data processing capability. Consequently, developing a compact, high-performance mode converter through efficient design methods is an urgent requirement. However, traditional design methodologies for these converters face significant computational complexities and inefficiencies. Addressing this challenge, this paper introduces a novel topology optimization design method for mode converters employing a Dynamic Adjustment of Update Rate (DAUR). This approach markedly reduces computational overhead, accelerating the design process while ensuring high performance and compactness. As a proof-of-concept, an ultra-compact dual-mode converter was designed. The DAUR method demonstrated an 80% reduction in computational time compared to traditional methods, while maintaining a compact design (only 1.4 μm × 1.4 μm) and an insertion loss under 0.68 dB across a wavelength range of 1525 nm to 1575 nm. Meanwhile, simulated inter-mode crosstalk remained below − 24 dB across a 40 nm bandwidth. A comprehensive comparison with traditional inverse design algorithms is presented, demonstrating our method’s superior efficiency and effectiveness. Our findings suggest that DAUR not only streamlines the design process but also facilitates exploration into more complex micro-nano photonic structures with reduced resource investment.

Intelligent Inversion Analysis of Surrounding Rock Parameters and Deformation Characteristics of a Water Diversion Surge Shaft

The water diversion surge shaft is vital for a hydropower station. However, the complex geological properties of the surrounding rock make it challenging to obtain its mechanical parameters. A method combining particle swarm optimization (PSO) and support vector machine (SVM) algorithms is proposed for estimating these parameters. According to the engineering geological background and support scheme, a three-dimensional model of the water diversion surge shaft is established by FLAC3D. An orthogonal test is designed to verify the accuracy of the numerical model. Then, the surrounding rock mechanical parameter database is established. The PSO-SVM intelligent inversion algorithm is used to invert the optimal values of the mechanical parameters of the surrounding rock. The support for excavating the next layer depends on the mechanical parameters of the current rock layer. An optimized design scheme is then compared and analyzed with the original support scheme by considering deformation and plastic characteristics. The research results demonstrate that the PSO-SVM intelligent inversion algorithm can effectively improve the accuracy and efficiency of the inversion of rock mechanical parameters. Under the influence of excavation, the surrounding rock in the plastic zone mainly fails in shear, with maximum deformation occurring in the middle and lower parts of the excavation area. The maximum deformation of the surrounding rock under support with long anchor cables is 0.6 cm less than that of support without long anchor cables and 4.07 cm less than that of support without an anchor. In the direction of the maximum and minimum principal stress, the maximum depth of the plastic zone under the support with long anchor cables is 1.3 m to 2.6 m less than that of the support without long anchor cables and the support without an anchor. Compared with the support without long anchor cables and support without an anchor, the support with long anchor cables can effectively control the deformation of the surrounding rock and limit the development of the plastic zone.

Guided wave tomography for quantitative thickness mapping using non-dispersive SH0 mode through geometrical full waveform inversion (GFWI)

Guided wave tomography plays a significantly important role in quantitatively mapping thickness variations in plate-like structures and pipelines in the petrochemical industry for accurate measurement of corrosion, as guided waves enable rapid screening of large areas without needing direct access. Several inverse algorithms have been implemented in guided wave tomography; however, almost all of them use a primary assumption: the three-dimensional (3D) guided wave thickness reconstruction is simplified as a two-dimensional (2D) acoustic wave velocity inversion, which is then mapped to thickness variation using the dispersive nature of guided waves. Although this assumption simplifies the inverse procedure, it makes it impossible to use non-dispersive modes in reconstructions. Geometrical full waveform inversion (GFWI) is promising to overcome this limitation since it can reconstruct corrosion profiles through geometry optimization using a data-fitting procedure, where velocity-to-thickness mapping is not needed. In this work, GFWI-based guided wave tomography is developed in plate-like structures, and is applied to reconstruct thickness maps in a series of corrosion defects using the non-dispersive SH0 mode, demonstrating high performance and achieving an improved reconstruction resolution.

Simultaneous measurement of carbon monoxide and carbon dioxide for combustion diagnosis using 2 μm laser absorption spectroscopy

AbstractCarbon monoxide (CO) and carbon dioxide (CO2) are products of incomplete combustion and complete combustion, respectively. Time‐resolved knowledge of CO and CO2 exhaust concentrations will aid in improving combustion strategies, control, and efficiency. To achieve online high‐precision simultaneous measurement of CO and CO2, a tunable diode laser absorption spectroscopy‐based sensor is designed and constructed. Two diode lasers with central wavelengths of 2.3 and 2.0 μm are multiplexed in time‐division to cover the absorption spectral lines of CO at 4285.00 cm−1 and CO2 at 4989.96 cm−1, respectively. Wavelength modulation spectroscopy with second harmonic detection normalized by the first harmonic (WMS‐2f/1f) is employed. A software lock‐in amplifier and inversion algorithm are implemented for data processing and concentration acquisition. The entire measurement system is based on the idea of a virtual instrument and is carried out using a high‐speed data acquisition card and a computer. Experimental verification demonstrates that the measurement accuracies of CO and CO2 were 2.47% and 2.56%, respectively, with a time resolution of 20 ms. Dynamic measurement experiments with an alcohol blast burner validate the feasibility of measuring CO and CO2 in actual combustion environments. The developed sensor demonstrates the potential for real‐time and in situ carbon emission measurement for combustion diagnosis.

High-Resolution Modeling of Aqueous Humor Dynamics in the Conventional Outflow Pathway of a Normal Human Donor Eye

Background and Objective: The conventional aqueous outflow pathway, which includes the trabecular meshwork (TM), juxtacanalicular tissue (JCT), and inner wall endothelium of Schlemm's canal (SC) and its basement membrane, plays a significant role in regulating intraocular pressure (IOP) by controlling aqueous humor outflow resistance. Despite its significance, the biomechanical and hydrodynamic properties of this region remain inadequately understood. Fluid-structure interaction (FSI) and computational fluid dynamics (CFD) modeling using high-resolution microstructural images of the outflow pathway provides a comprehensive method to estimate these properties under varying conditions, offering valuable understandings beyond the capabilities of current imaging techniques.Methods: In this study, we utilized high-resolution 3D serial block-face scanning electron microscopy (SBF-SEM) to image the TM/JCT/SC complex of a normal human donor eye perfusion-fixed at an IOP of 7 mm Hg. We developed a detailed 3D finite element (FE) model of the pathway using SBF-SEM images to simulate the biomechanical environment. The model included the TM/JCT/SC complex (structure) with interspersed aqueous humor (fluid). We employed a 3D, inverse FE algorithm to calculate the unloaded geometry of the TM/JCT/SC complex and utilized FSI to simulate the pressurization of the complex from 0 to 15 mm Hg.Results: Our simulations revealed that the resultant velocity distribution in the aqueous humor across the TM/JCT/SC complex is heterogeneous. The JCT and its deepest regions, specifically the basement membrane of the inner wall of SC, exhibited a volumetric average velocity of ∼0.011 mm/s, which is higher than the TM regions, with a volumetric average velocity of ∼0.007 mm/s. Shear stress analysis indicated that the maximum shear stress, based on our FE code criteria, was 0.5 Pa starting from 10 µm into the TM from the anterior chamber and increased to 0.95 Pa in the JCT and its adjacent SC inner wall basement membrane. Also, the tensile stress and strain distributions showed significant variations, with the first principal stress reaching up to 57 Pa (compressive volumetric average) and the first principal strain reaching up to 3.5% in areas of high mechanical loading. The resultant stresses, strains, and velocities exhibited relatively similar average values across the TM, JCT, and SC regions, primarily due to the uniform elastic moduli assigned to these components. Our computational fluid dynamics (CFD) analysis revealed that while the velocity of the aqueous humor remained consistent, the maximum shear stress was reduced by a factor of thirty.Conclusion: The uneven distribution of shear stress and velocity within the TM/JCT/SC complex highlights the complex biomechanical environment that regulates aqueous humor outflow.

A hybrid inversion algorithm to obtain the resistivity of the uninvaded zone based on the array induction log

This study investigates the impact of the drilling mud invasion on the borehole-measured resistivity. The primary objective is to retrieve the true resistivity of the formation, which helps in identifying different fluids in the reservoir. To achieve this goal, We proposed a hybrid inversion approach integrating the Levenberg-Marquardt and Markov Chain Monte Carlo algorithms with a five-parameter formation resistivity model. Synthetic and real-world data are utilized to assess the method's robustness and reliability. The simulated result indicated that the method is reliable when the data noise level is less than 5%.The method applied to real-world data revealed that the resistivity profile on the water zone showed a slight increase in the inverted resistivity from measured resistivity. Meanwhile, in the oil zone, the calculated resistivity revealed a high deviation from the measured resistivity, indicating the effects of mud invasion. The introduced methods are only applicable when the invasions of mud occur within the range of the logging tool's depth of investigation. Moreover, the method may give no reliable result when the invasion exceeds the tool's investigation depth. It indicates its limitation.

Unconstrained measurement method and verification of thrust vector in small solid propulsion system

In response to the inherent limitations of traditional thrust vector measurement methods for small solid rocket motors(SRM), this paper proposes an innovative method based on flight attitude inversion. Flight measurement tests were conducted. Firstly, a six-degree-of-freedom (6-DOF) data inversion algorithm for solving the dynamic data of the three-axis thrust vector was constructed based on the Euler transformation method and the 6-DOF flight motion mathematical model of the flight measurement platform under the action of a three-axis thrust vector. Then, an unconstrained experimental platform was established, obtaining 6-DOF data during the operation of the experimental SRM through an inertial measurement unit(IMU). Finally, the thrust vector data were obtained from the recorded data. During the stable working phase, the average main thrust was 845 N, and the average thrust eccentricity angle was 0.018°, with a main thrust error of 0.6 %, thereby validating the feasibility of the measurement method.

A GPR layered media parameters inversion method under rough surface

Abstract Ground Penetrating Radar (GPR) plays an important role in pavement detection and road exploration due to its efficiency. Traditional media parameter inversion algorithms only consider ideal smooth surfaces and neglect the roughness of interfaces, leading to significant errors in practical applications. Therefore, a GPR rough surface-layered medium parameter inversion method based on genetic algorithm is proposed in this paper. The method uses the generalized reflection coefficient and considers the influence of the surface roughness of the medium. Then, a radar echo signal time-domain model is established. Finally, the cost function is optimized by genetic algorithm. The effectiveness and accuracy are validated and analysed by utilizing simulated data through random rough surfaces models.