Simple Inversion Procedure Research Articles

Imaging of the internal structure of an asteroid analogue from quasi-monostatic microwave measurement data

Context.The internal structure of small Solar System bodies (SSSBs) is still poorly understood, although it can provide important information about the formation process of asteroids and comets. Space radars can provide direct observations of this structure.Aims.In this study, we investigate the possibility to infer the internal structure with a simple and fast inversion procedure applied to radar measurements. We consider a quasi-monostatic configuration with multiple measurements over a wide frequency band, which is the most common configuration for space radars. This is the first part (Paper I) of a joint study considering methods to analyse and invert quasi-monostatic microwave measurements of an asteroid analogue. This paper focuses on the frequency domain, while a separate paper focuses on time-domain methods.Methods.We carried out an experiment in the laboratory equivalent to the probing of an asteroid using the microwave analogy (multiplying the wavelength and the target dimension by the same factor). Two analogues based on the shape of the asteroid 25143 Itokawa were constructed with different interiors. The electromagnetic interaction with these analogues was measured in an anechoic chamber using a multi-frequency radar and a quasi-monostatic configuration. The electric field was measured on 2372 angular positions (corresponding to a sampling offering complete information). We then inverted these data with two classical imaging procedures, allowing us to reach the structural information of the analogues interior. We also investigated reducing the number of radar measurements used in the imaging procedures, that is both the number of transmitter-receiver pairs and the number of frequencies.Results.The results show that the 3D map of the analogues can be reconstructed without the need for a reference target. Internal structural differences are distinguishable between the analogues. This imaging can be achieved even with a reduced number of measurements. With only 35 well-selected frequencies over 321 and 1257 transmitter-receiver pairs, the reconstructions are similar to those obtained with the entire frequency band.

A Distance-Geometric Method for Recovering Robot Joint Angles From an RGB Image

Autonomous manipulation systems operating in domains where human intervention is difficult or impossible (e.g., underwater, extraterrestrial or hazardous environments) require a high degree of robustness to sensing and communication failures. Crucially, motion planning and control algorithms require a stream of accurate joint angle data provided by joint encoders, the failure of which may result in an unrecoverable loss of functionality. In this paper, we present a novel method for retrieving the joint angles of a robot manipulator using only a single RGB image of its current configuration, opening up an avenue for recovering system functionality when conventional proprioceptive sensing is unavailable. Our approach, based on a distance-geometric representation of the configuration space, exploits the knowledge of a robot's kinematic model with the goal of training a shallow neural network that performs a 2D-to-3D regression of distances associated with detected structural keypoints. It is shown that the resulting Euclidean distance matrix uniquely corresponds to the observed configuration, where joint angles can be recovered via multidimensional scaling and a simple inverse kinematics procedure. We evaluate the performance of our approach on real RGB images of a Franka Emika Panda manipulator, showing that the proposed method is efficient and exhibits solid generalization ability. Furthermore, we show that our method can be easily combined with a dense refinement technique to obtain superior results.

Average-chain behavior of isotropic incompressible polymers obtained from macroscopic experimental data. A simple structure-based WYPiWYG model in Julia language

Elastomeric materials and soft biological tissues are made up of synthetic and protein fibers, respectively. The uncoiling of these fibers during loading produces a non-linear elastic macroscopic behavior in the regime of finite strains. Many hyperelastic models have been developed to reproduce this behavior assuming the existence of a strain energy function. In structure-based models, the analytical energy function is obtained from the stored energy of all the material constituents. This stored energy is given frequently by the entropy of the chain network obtained from Langevin statistical treatment of the possible configurations adopted by the chains, and a representative cell for their spatial distribution. One of the most used models is the eight chain model, being its salient feature that it reproduces the overall response of isotropic hyperelastic materials with only two material parameters obtained from a tensile test. On the other hand, in WYPiWYG hyperelasticity the stored energies are numerical instead of analytical and capture, to any precision, the experimental tests on the material. However, due to their phenomenological nature, their determination requires more tests. In this work, we develop a microstructure-based WYPiWYG hyperelastic model in which the average chain behavior is obtained from macroscopic tests through a simple automatic inverse procedure. We show that, without assuming a probability distribution function nor any particular chain arrangement, we obtain, at the same computational cost, better predictions than the 8-chain model. Code of the model and of the examples in the Julia programming language are included.

A Robust Inversion Algorithm for Surface Leaf and Soil Temperatures Using the Vegetation Clumping Index

The inversion of land surface component temperatures is an essential source of information for mapping heat fluxes and the angular normalization of thermal infrared (TIR) observations. Leaf and soil temperatures can be retrieved using multiple-view-angle TIR observations. In a satellite-scale pixel, the clumping effect of vegetation is usually present, but it is not completely considered during the inversion process. Therefore, we introduced a simple inversion procedure that uses gap frequency with a clumping index (GCI) for leaf and soil temperatures over both crop and forest canopies. Simulated datasets corresponding to turbid vegetation, regularly planted crops and randomly distributed forest were generated using a radiosity model and were used to test the proposed inversion algorithm. The results indicated that the GCI algorithm performed well for both crop and forest canopies, with root mean squared errors of less than 1.0 °C against simulated values. The proposed inversion algorithm was also validated using measured datasets over orchard, maize and wheat canopies. Similar results were achieved, demonstrating that using the clumping index can improve inversion results. In all evaluations, we recommend using the GCI algorithm as a foundation for future satellite-based applications due to its straightforward form and robust performance for both crop and forest canopies using the vegetation clumping index.

Simple and effective failure analysis of dissimilar resistance spot welded advanced high strength steel sheets

The failure of welded structures was analyzed considering dissimilar combinations of advanced high strength steels (AHSS) and a conventional mild steel. A method to characterize the mechanical properties of hardening behavior along with the deterioration associated with micro-void development and fracture criterion based on a modified damage model was applied by employing simple but effective experimental and numerical inverse procedure. The proposed procedure was solely based on standard and miniature simple tension tests for base sheets and weld nuggets, respectively. The identified plastic and failure properties were applied to the analysis of the failure mode and strength in the two well-accepted coupon tests of lap-shear and U-shape tension tests for DP980-TRIP980 and GMW2-TRIP980 dissimilar welded sheets. The analysis confirmed that the distinct failure behavior in the coupon tests for the two dissimilar weld cases was mainly due to the competition between the element with high strength/low ductility and the element with low strength/high ductility.

Bayesian estimate of pre-mixed and diffusive rate of heat release phases in marine diesel engines

The rate of heat released during the combustion in Diesel engines is important for many reasons, including performance evaluation, pollutant formation, and control. Combustion in Diesel engines can be generally divided into three phases: pre-mixed, diffusive or mixed-controlled, and late combustion. The objective of this paper is to estimate the rate of heat released by the fuel in a marine Diesel engine, in order to identify the pre-mixed and diffusive phases, using the Sampling Importance Resampling (SIR) Bayesian Particle Filter. Experimental pressure data obtained from a piezoelectric sensor, installed in a research marine diesel engine (MAN Innovator 4c), was used to feed the observation model in such Bayesian approach. The evolution model for the pressure was formulated in terms of a set of ordinary differential equations, coming from the First Law of Thermodynamics, together with a random walk model for the unknown state variable. The proposed approach was able to identify the pre-mixed and diffusive combustion phases, for different engine loads. Results were compared with a simple inversion procedure, showing a good agreement. The combustion ignition delay was also calculated, showing its variation with the engine load.

Results of matched-field inversion in a three-dimensional oceanic environment ignoring horizontal refraction

For some practical reasons, inverse problems in ocean acoustics are often based on 2-D modeling of sound propagation, hence ignoring 3-D propagation effects. However, the acoustic propagation in shallow-water environments, such as the continental shelf, may be strongly affected by 3-D effects, thus requiring 3-D modeling to be accounted for. In the present talk, the feasibility and the limits of an inversion in fully 3-D oceanic environments assuming 2-D propagation are investigated. A simple matched-field inversion procedure implemented in a Bayesian framework and based on the exhaustive search of the parameter space is used. The study is first carried out on a well-established wedge-like synthetic test case, which exhibits well-known 3-D effects. Both synthetic data and replica are generated using a parabolic-equation-based code. This approach highlights the relevance of using 2-D propagation models when inversions are performed at relatively short ranges from the source. On the other hand, important mismatch occurs when inverting at farther ranges, demonstrating that the use of fully 3-D forward models is required. Results of inversion on experimental small-scale data, based on a subspace approach as suggested by the preliminary study made on the synthetic test case, are presented.

A Planar Transmission-Line Sensor for Measuring the Microwave Permittivity of Liquid and Semisolid Biological Materials

A planar transmission-line configuration for rapid, nondestructive, wideband permittivity measurements of liquid and semisolid materials at microwave frequencies is described. The transmission-line propagation constant of the proposed configuration is determined with the multiline technique from scattering parameter measurements of two lines with a known length difference. Guidelines for the appropriate selection of the line dimensions and a technique for resolving the phase ambiguity associated with the multiline technique are presented. The material permittivity is related to the propagation constant by closed-form expressions that allow the permittivity to be determined by a relatively simple numerical inversion procedure. The proposed sensor has the advantage of not requiring the sample to have uniform edges, nor that they are perpendicular to the planar line. The technique used for determining the line propagation constant has the advantage of not requiring any transmission-line discontinuities to be explicitly modeled. To illustrate the technique, a coplanar waveguide transmission-line sensor was fabricated and used to measure the permittivity of six liquids and four gelatin samples from 1 to 5 GHz. These measurements agree very well with coaxial-line probe measurements, demonstrating the accuracy of the proposed configuration. The sensitivity of the results to dimensional tolerances is demonstrated.

Multiannual changes of CO<sub>2</sub> emissions in China: indirect estimates derived from satellite measurements of tropospheric NO<sub>2</sub> columns

Abstract. Multiannual satellite measurements of tropospheric NO2 columns are used for evaluation of CO2 emission changes in China in the period from 1996 to 2008. Indirect top-down annual estimates of CO2 emissions are derived from the satellite NO2 column measurements by means of a simple inverse modeling procedure involving simulations performed with the CHIMERE mesoscale chemistry–transport model and the CO2-to-NOx emission ratios from the Emission Database for Global Atmospheric Research (EDGAR) global anthropogenic emission inventory and Regional Emission Inventory in Asia (REAS). Exponential trends in the normalized time series of annual emissions are evaluated separately for the periods from 1996 to 2001 and from 2001 to 2008. The results indicate that the both periods manifest strong positive trends in the CO2 emissions, and that the trend in the second period was significantly larger than the trend in the first period. Specifically, the trends in the first and second periods are best estimated to be in the range from 3.7 to 8.3 and from 11.0 to 13.2% per year, respectively, taking into account statistical uncertainties and differences between the CO2-to-NOx emission ratios from the EDGAR and REAS inventories. Comparison of our indirect top-down estimates of the CO2 emission changes with the corresponding bottom-up estimates provided by the EDGAR (version 4.2) and Global Carbon Project (GCP) glomal emission inventories reveals that while acceleration of the CO2 emission growth in the considered period is a common feature of both kinds of estimates, nonlinearity in the CO2 emission changes may be strongly exaggerated in the global emission inventories. Specifically, the atmospheric NO2 observations do not confirm the existence of a sharp bend in the emission inventory data time series in the period from 2000 to 2002. A significant quantitative difference is revealed between the bottom-up and indirect top-down estimates of the CO2 emission trend in the period from 1996 to 2001 (specifically, the trend was not positive according to the global emission inventories, but is strongly positive in our estimates). These results confirm the findings of earlier studies that indicated probable large uncertainties in the energy production and other activity data for China from international energy statistics used as the input information in the global emission inventories. For the period from 2001 to 2008, some quantitative differences between the different kinds of estimates are found to be in the range of possible systematic uncertainties associated with our estimation method. In general, satellite measurements of tropospheric NO2 are shown to be a useful source of information on CO2 sources collocated with sources of nitrogen oxides; the corresponding potential of these measurements should be exploited further in future studies.

Three‐dimensional numerical analysis of steady state pumping tests in heterogeneous confined aquifers

We study three‐dimensional steady state flow field generated by a fully penetrating well extracting a constant water discharge from a confined aquifer of constant thickness. The hydraulic conductivity K is modeled as an axisymmetric, stationary random space function, and the flow equation is solved by using the seven‐node finite volume numerical scheme. In view of application in aquifer characterization we analyze how the equivalent conductivity Keq varies as a function of the distance from the extraction well. The numerical simulations showed that the boundary condition at the well exerts a large impact on Keq and that the first‐order solution in σY2 obtained by Indelman et al. (1996) is valid up to σY2 = 0.5. For higher values of σY2 the first‐order solution overestimates Keq with differences that for a given σY2, reduce progressively as the formation becomes more anisotropic. A simple inverse procedure based on Keq, obtained through cross‐well interference, is finally proposed and tested with the objective of estimating the parameters of the geostatistical model of variability of the hydraulic conductivity. A few parametric examples showed that a suitable interpretation of pumping tests can be used to safely estimate parameters such as the geometric mean of the hydraulic conductivity, its variance, and, although with larger uncertainty, the horizontal integral scale, while the inference of the anisotropy ratio is highly uncertain and error prone.

A simple inverse procedure to determine heat flux on the tool in orthogonal cutting

The applications of numerical simulation to machining processes have been more and more increasing in the last decade: today, a quite effective predictive capability has been reached, at least as far as global cutting variables (for instance cutting forces) are concerned. On the other hand, the capability to predict local cutting variables (i.e. stresses acting on the tool, temperature distribution, residual stresses in the machined surface) has to be furtherly improved, as well as effective experimental procedures to validate numerical results have to be developed. The aim of this paper is the proposition of an innovative approach, based on an simple inverse procedure, in order to identify both the heat flux flowing into the tool through the rake face and the heat transfer coefficient between the tool and the environment during a typical orthogonal cutting process. It is worth pointing out that the effective determination of such quantities is necessary in order to carry out a reliable prediction of the temperature distribution in the tool during the process. The procedure is based on the integration of numerical simulations, inverse approach algorithms and experimental tests.

Dynamic Imaging of Nuclear Wave Functions with Ultrashort UV Laser Pulses

Non-Born-Oppenheimer supercomputer simulations of dissociative ionization of H2(+) with an ultrashort (t(p) < 15 fs), intense UV (lambda = 30, 60 nm) laser pulse are used to illustrate the imaging of nuclear motion. The resulting kinetic energy spectra of protons from Coulomb explosion lead by a simple inversion procedure to reconstruction of the initial nuclear probability distribution, i.e., laser Coulomb explosion imaging. Simultaneously, kinetic energy spectra of the ionized electron lead by energy conservation to the same reconstruction of the initial nuclear probability distribution, by laser photoelectron imaging.

Simple inversion procedure for shallow seismic refraction in continuously nonhomogeneous soils

Seismic refraction analysis is presented for uniformly deposited shallow soil strata with wave velocity increasing continuously with depth due to differential compaction effects. Closed form solutions of the surface-to-surface travel time as well as for the depth to maximum penetration are derived for realistic velocity-depth functions. An inversion procedure based on simple formulas is presented and its applicability is demonstrated and discussed. The method takes into account the information along the entire refraction line in one step, in contrast to the discrete ray-tracing technique and is, therefore, less sensitive to the natural scatter of the data.

Recovering the Intrinsic Metallicity Distribution of Elliptical Galaxies

We present a simple recipe to derive the metallicity distribution of galaxies as a function of their integrals of the motion. Elliptical galaxies are known to possess metallicity gradients that frequently show variations of a factor of 2 from the center to the effective radius (Peletier, 1989). The observed gradients are the result of projection and orbital mixing. Orbital mixing arises because stars at a given radius may have their apocenters spanning a wide range of radii. Thus, the mean metallicity at any given point inside the galaxy is the result of the metallicity distribution in phase space weighted by the galaxian distribution function. We have proposed (Ciotti, Stiavelli &amp; Braccesi, 1995) a simple inversion procedure allowing one to derive the dependence of metallicity on the integrals of motion for a spherical galaxy. The ideas of this paper can be generalized to oblate two-integrals models following the Hunter &amp; Qian (1993) technique.

Real-time inverse kinematics of the human arm.

A simple inverse kinematics procedure is proposed for a seven degree of freedom model of the human arm. Two schemes are used to provide an additional constraint leading to closed-form analytical equations with an upper bound of two or four solutions. Multiple solutions can be evaluated on the basis of their proximity from the rest angles or the previous configuration of the arm. Empirical results demonstrate that the procedure is well suited for real-time applications.

Recovering the intrinsic metallicity distribution of elliptical galaxies

We present a simple recipe to derive the metallicity distribution of galaxies as a function of their integrals of the motion. Elliptical galaxies are known to possess metallicity gradients that frequently show variations of a factor of 2 from the center to the effective radius (Peletier, 1989). The observed gradients are the result of projection and orbital mixing. Orbital mixing arises because stars at a given radius may have their apocenters spanning a wide range of radii. Thus, the mean metallicity at any given point inside the galaxy is the result of the metallicity distribution in phase space weighted by the galaxian distribution function. We have proposed (Ciotti, Stiavelli & Braccesi, 1995) a simple inversion procedure allowing one to derive the dependence of metallicity on the integrals of motion for a spherical galaxy. The ideas of this paper can be generalized to oblate two-integrals models following the Hunter & Qian (1993) technique.

Weak elastic anisotropy and the tube wave

Tube‐wave speed in the presence of a weakly anisotropic formation can be expressed in terms of an effective shear modulus for an equivalent isotropic formation. When combined with expressions for the speeds of the SH‐ and quasi‐SV‐waves along the borehole axis, a simple inversion procedure can be obtained to determine three of the five elasticities of a transversely isotropic (TI) formation tilted at some known angle with respect to the borehole axis. Subsequently, a fourth combination of elastic moduli can be estimated from the expression for the qP‐wave speed along the borehole axis. The possibility of determining all five elasticities of a TI formation based on an assumed correlation between two anisotropy parameters is discussed.

Density profiles of concentrated colloidal suspensions in sedimentation equilibrium

Sedimentation equilibria in concentrated colloidal suspensions are studied within the framework of density functional theory for inhomogeneous fluids. The density profile in the gravitational field is calculated exactly for the one-dimensional model of hard rods. The predictions of the local density approximation agree very well with coarse-grained density profiles derived from extensive Monte Carlo simulations of three-dimensional systems of hard spheres and charge-stabilized colloidal particles. The simulations show that the shape of the density profiles is very sensitive to the nature of the interactions between colloidal particles, and allow a direct test of a simple inversion procedure, which extracts the osmotic equation of state of colloidal suspensions from a measurement of their density profile. The method is sufficiently sensitive to allow the crystal-fluid tie line to be located at high colloid concentrations. The local density approximation is generalized to calculate density profiles of bidisperse hard sphere suspensions; the competition between gravity and entropy leads to nonmonotonic density profiles which are sensitive to the mass ratio, for a given size ratio. The density functional approach and Monte Carlo simulations are finally extended to study the effect of interparticle attractions on the density profiles, which exhibit a region of rapid variation corresponding to the ‘‘liquid-gas’’ interface for sufficiently strong attractive interactions.

A realistic torso model for magnetocardiography

This paper contains the description of an inhomogeneous, multi-compartmental volume conductor model which is in use in our group. Although initially developed for the study of the ECG, it has been found to serve equally well for simulating the magnetocardiogram (MCG), the forward problem, and as a basis for source analysis of the MCG, the inverse problem. For both problems some illustrative examples are included demonstrating the necessity of using an inhomogeneous volume conductor model of the torso, having realistic--preferably tailored--geometry. A simple inverse procedure, based on correlation techniques, is included for the solution of the problem of source localization when an accurate description of the inhomogeneous volume conductor is available.

Determination of vegetation canopy parameters from optical measurements

Special measurements of barley and clover canopy directional reflectance in the red and NIR spectral regions during vegetative growth were carried out to test the Nilson-Kuusk canopy reflectance model. The model reproduces adequately the measured angular distribution of red reflectance. Systematic differences are observed in the NIR spectral region. Using a simple inversion procedure, the canopy optical and structural parameters are determined from optical reflectance measurements in one or two spectral regions. The results of inversion agree reasonably well with those of phytometric measurements. The disagreement between the measured and calculated NIR reflectance profiles gives rise to difficulties in inversion in NIR channel, and this is the reason why simultaneous measurements in two spectral regions had no advantage in model parameter estimation. Obviously, the Nilson-Kuusk model needs some improvement in the NIR spectral region.