Statistical Inversion Research Articles

The Influence of Greenhouse Effect on Earth’s Atmosphere Based on Artificial Intelligence

Greenhouse gases absorb and release a large amount of ground thermal radiation, and modify part of the energy between the earth and the atmosphere, so that it has a greenhouse effect. It is the main cause of global warming and climate anomaly caused by modern human activities. In order to solve the shortcomings of the existing research on the impact of greenhouse effect on the Earth’s atmosphere, this paper briefly introduces the numerical methods of radiation and heat conduction coupling, the components of the Earth’s atmosphere, and the sources and sinks of greenhouse gases. The calculation and analysis of spectral absorption coefficient and the configuration of super parameters of depth learning model are discussed. A numerical simulation of carbon dioxide concentration based on depth learning is constructed and the C02 concentration profile is calculated using the C02 statistical inversion flow of principal component analysis. The calculated temperatures of the standard atmosphere and the standard atmosphere with the carbon dioxide concentration doubled were compared. The data showed that the temperature in the upper stratosphere rose to 58.

Development of the Sanya Incoherent Scatter Radar and Preliminary Results

AbstractLed by the Institute of Geology and Geophysics, Chinese Academy of Sciences, we have built a brand‐new modular active digital phased array, with all solid‐state transmission and digital receiving incoherent scatter radar (ISR) in Sanya (18.3°N, 109.6°E), a station in low latitude China called Sanya ISR (SYISR) since 2015. The development of SYISR involved the indoor design and development of key components, an outdoor prototype test, and the production and debugging of the entire array. The unique features of SYISR include a single‐channel directly connected T/R unit and antenna, a radar array monitoring and calibration network, environmental adaptability design and open architecture. The entire radar has 4,096 channels and 5,930 modules in total. All the technical indices, mainly including a >2 MW peak power, a 43 dBi antenna gain and a <120 K noise temperature, either meet or are superior to the designed value through an independent evaluation. Waveforms of single pulse, linear frequency modulation, Barker code, long pulse and alternating code have been implemented to meet multiple purposes. Four observational modes for ionospheric experiments, including zenith stare, perpendicular to geomagnetic field, meridian scan, and all sky scan, have been developed. We have implemented time domain decoding, frequency domain decoding, and statistical inversion methods in calculating the autocorrelation function and power spectra in signal processing. The preliminary experimental results on ionospheric parameters, plasma lines, irregularities and hard targets are reasonable and encouraging, which greatly enhances our confidence in achieving our scientific goals in the future.

Dynamical Features of Isolated Two- and Three-Level Atoms Interacting with a Cavity Field

Some dynamical features of two- and three-level atoms interacting locally with an ideal cavity field are investigated. These dynamical features are introduced by employing the statistical atomic inversion, entropy squeezing, and tomographic entropy. Our results show that the initial setting states play an essential role in the temporal evolution of the three quantities. The sensitivity of the two-level atomic state is less than that depicted by the three-level atom. The initial state has a small impact on the two types of entropies for the two-level atom. However, it has an appreciable effect in the case of the three-level atom for different regulations of the initial atomic state.

Correlated Sample-Based Prior in Bayesian Inversion Framework for Microwave Tomography

When using the statistical inversion framework in microwave tomography (MWT), generally, the real and imaginary parts of the unknown dielectric constant are treated as uncorrelated and independent random variables. Thereby, in the maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> estimates, the two recovered variables may show different structural changes inside the imaging domain. In this work, a correlated sample-based prior model is presented to incorporate the correlation of the real part with the imaginary part of the dielectric constant in the statistical inversion framework. The method is used to estimate the inhomogeneous moisture distribution (as dielectric constant) in a large cross section of polymer foam. The targeted application of MWT is in industrial drying to derive intelligent control methods based on tomographic inputs for selective heating purposes. One of the features of the proposed method shows how to integrate lab-based dielectric characterization, often available in MWT application cases, in the prior modeling. The method is validated with numerical and experimental MWT data for the considered moisture distributions.

Hierarchical deconvolution for incoherent scatter radar data

Abstract. We propose a novel method for deconvolving incoherent scatter radar data to recover accurate reconstructions of backscattered powers. The problem is modelled as a hierarchical noise-perturbed deconvolution problem, where the lower hierarchy consists of an adaptive length-scale function that allows for a non-stationary prior and as such enables adaptive recovery of smooth and narrow layers in the profiles. The estimation is done in a Bayesian statistical inversion framework as a two-step procedure, where hyperparameters are first estimated by optimisation and followed by an analytical closed-form solution of the deconvolved signal. The proposed optimisation-based method is compared to a fully probabilistic approach using Markov chain Monte Carlo techniques enabling additional uncertainty quantification. In this paper we examine the potential of the hierarchical deconvolution approach using two different prior models for the length-scale function. We apply the developed methodology to compute the backscattered powers of measured polar mesospheric winter echoes, as well as summer echoes, from the EISCAT VHF radar in Tromsø, Norway. Computational accuracy and performance are tested using a simulated signal corresponding to a typical background ionosphere and a sporadic E layer with known ground truth. The results suggest that the proposed hierarchical deconvolution approach can recover accurate and clean reconstructions of profiles, and the potential to be successfully applied to similar problems.

Influence of an External Classical Field on a ♢ Four-Level Atom Inside a Quantized Field

In this paper, we study the effect of detuning parameters and driven external classical field parameters on a quantum system consisting of a ♢-configuration four-level atom inside a quantized cavity field. Under some canonical conditional of dressed states, the exact solution of the Schrödinger equation is obtained. The occupation of atomic levels and statistical population inversion is studied. Our results show that the classical field parameter dissolved the collapse periods and increased the maximum bounds of the upper state, while decreasing the lower bounds of the lower state. The detuning parameters reduce the minimum bounds of atomic levels and their inversion. On the other hand, the linear entropy and l1 norm of coherence are employed to measure the temporal evolution of the mixedness and coherence. It is found that the driven classical field improves the temporal evolution of the mixedness and lower bounds of coherence. However, the detuning parameters have a destructive effect on the mixedness and lower bounds of coherence. The intensity of the external classical field is regarded as a control parameter with different values of detuning parameters.

Statistical inverse estimation of source terms in the Helmholtz equation

In this paper, we study source identification for Helmholtz equation by using statistical inversion method. The approximate solutions are obtained from samples measured on the random boundary of the radiated electric field. Error estimates of exact solutions and their approximations are proven, and the validity of the methods is verified by numerical experiments.

Development of 222Rn Emanation Sources with Integrated Quasi 2π Active Monitoring.

In this work, a novel approach for the standardization of low-level 222Rn emanation is presented. The technique is based on the integration of a 222Rn source, directly, with an α-particle detector, which allows the residual 222Rn to be continuously monitored. Preparation of the device entails thermal physical vapor deposition of 226RaCl2 directly onto the surface of a commercially available ion implanted Si-diode detector, resulting in a thin-layer geometry. This enables continuous collection of well resolved α-particle spectra of the nuclei, decaying within the deposited layer, with a detection efficiency of approximately 0.5 in a quasi 2π geometry. The continuously sampled α-particle spectra are used to derive the emanation by statistical inversion. It is possible to achieve this with high temporal resolution due to the small background and the high counting efficiency of the presented technique. The emanation derived in this way exhibits a dependence on the relative humidity of up to 15% in the range from 20% rH to 90% rH. Traceability to the SI is provided by employing defined solid-angle α-particle spectrometry to characterize the counting efficiency of the modified detectors. The presented technique is demonstrated to apply to a range covering the release of at least 1 to 210 222Rn atoms per second, and it results in SI-traceable emanation values with a combined standard uncertainty not exceeding 2%. This provides a pathway for the realization of reference atmospheres covering typical environmental 222Rn levels and thus drastically improves the realization and the dissemination of the derived unit of the activity concentration concerning 222Rn in air.

Using statistical inverse methods for detecting defects in electronic components

The thermal modeling of electronic components is mandatory to optimize the cooling design versus reliability. Indeed most of failures are due to thermal phenomena [1]. Some of them are neglected or omitted by lack of data: ageing, manufacturing issues like voids in glue or solder joints, or material properties variability. Transient measurements of the junction-to-board temperature supply real thermal behavior of the component and PCB assembly to complete these missing data[2]. To complement and supplement the numerical model, inverse methods identification based on a statistical deconvolution approach, such as Bayesian one, is applied on these measurements to extract a Foster RC thermal network. The identification algorithm performances have been demonstrated on numerical as well as experimental dataset. Furthermore defects or voids can be detected using the extracted Foster RC networks.

Statistical Inversion Approach for Stress Estimation Based on Strain Monitoring in Continuously Pre-Stressed Concrete Beams

Stress is one of the most important physical indexes reflecting the mechanical behavior of concrete structures. In general, stress in structures cannot be directly monitored and can only be estimated through an established model of stress and strain. The accuracy of the estimated stress depends on the rationality of the established model for stress and strain. As the strain measured by sensors contains creep, shrinkage, and elastic strain, it is difficult to establish an analytical model for strain and stress. In this paper, a statistical inverse method was utilized to estimate the stress in continuously pre-stressed concrete beams based on the monitored strain. Stress in the beams and the model uncertainty factors were treated as model parameters. A linear-simplified method was adopted to determine the prior distribution of the stresses. The posterior distribution of the stresses at different locations during bridge construction can be obtained by the proposed method. A continuously pre-stressed concrete beam bridge was taken as the case study to verify the effectiveness of the proposed method. Additionally, the constitution of the total strain in the different construction stages was calculated. It was concluded that the creep strain is the dominant part of the total strain.

Statistical characterization of low-porosity, additively manufactured metal foams measured in an acoustic impedance tube

This work focuses on the acoustic response of aluminum foams with different porosities additively manufactured using powder bed fusion. Emerging voxel-by-voxel additive manufacturing, which further expands the achievable microstructure design space through localized spatial control of the printing properties, allows for direct fabrication of samples with varying percent porosities. Unlike traditional, rigid-frame foams with very high porosities, the samples range from fully dense to approximately 50% porosity. This work utilizes normal incidence acoustic impedance tube measurements and the Johnson–Champoux–Allard–Lafarge analytic model, which are common characterization methods for traditional rigid-frame porous media. For the reflection and transmission coefficients measured in an acoustic impedance tube, Bayesian statistical inversion is performed with the Johnson–Champoux–Allard–Lafarge model to obtain distributions of the possible values for the six required model parameters. By using a statistical characterization approach, the applicability of these common acoustic measurement and modeling methods for lower porosity additively manufactured foams is also assessed. [This work was supported by the Office of Naval Research.]

Nonstationary bubble shape determination in Electrical Impedance Tomography combining Gauss–Newton Optimization with particle filter

Electrical Impedance Tomography (EIT) is a technique utilized in multiphase flow for identifying flow patterns and void-fraction calculation. An image made of the conductivity of the domain is formed by combining an inverse problem and measurements. Recursive statistical inversion, such as the particle filters, is scarce when dealing with EIT. For that matter, it is proposed a recursive Gauss–Newton Optimization Sequential Importance Resampling (GNOSIR) filter aimed to reconstruct vertical slug flow. It combines the Optimization with an Image Processing algorithm to improve the prior information when the posterior density is far from likelihood. The Level Set Method describes the contour of the inclusion using an elliptical Level Set Function to avoid the curse of dimensionality. Results demonstrate that the GNOSIR filter improves the estimation when there is a sudden and fast evolution of the inclusion’s contour between states.

A synergic study on estimating surface downward shortwave radiation from satellite data

Surface downward shortwave radiation (DSR) is a fundamental variable in determining the Earth's radiation balance and is essential in many applications. Considerable efforts have been devoted to algorithm development, product generation, and validation. However, few studies have focused on comparing retrieval approaches, examining their strengths and weaknesses, and identifying the most suitable scenarios for each approach. In this study, we implemented and evaluated five representative DSR retrieval algorithms, including the forward parameterization approach, two physical inversion methods (look-up table (LUT) and optimization), and two statistical inversion methods (direct estimation and neural networks). We then proposed an algorithm-integration framework that combined the results of these DSR retrieval methods to further improve DSR estimation accuracy and consistency. To validate the DSR retrievals, we used in-situ data collected at 25 stations of the Baseline Surface Radiation Network (BSRN) over one year. Validation revealed that forward parameterization consistently performed best, with an overall root mean square error (RMSE) of 91.7 W/m2 or a relative RMSE of 16.9%, although it generated the fewest valid retrievals. For an identical data set, the LUT approach generated results comparable to those of parameterization. The neural network-based algorithm-integration approach reduced the RMSE by 11.0 W/m2 or the relative RMSE by 2.0%, compared to the best individual retrieval algorithm. Our analysis demonstrates that algorithm integration is a promising way to obtain DSR data that are superior to estimates from any individual retrieval algorithm.

Bayesian inversion for a fractional Lotka-Volterra model: An application of Canadian lynx vs. snowshoe hares

The Bayesian statistical inversion method is implemented to obtain the parameter estimations for fractional LotkaVolterra models, including the derivative orders, based on analytical solutions obtained by the multi-step homotopy method. For the posterior distributions of the parameter of interest, we used Markov Chain Monte Carlo method through the JAGS package within R software. The posterior predictive model–checking method is implemented to select the best model for a real data set.

Deterministic and statistical methods for the characterisation of poroelastic media from multi-observation sound absorption measurements

This paper proposes a framework for the estimation of the transport and elastic properties of open-cell poroelastic media based on sound absorption measurements. The sought properties are the Biot-Johnson-Champoux-Allard model parameters, namely five transport parameters, two elastic properties and the mass density, as well as the sample thickness. The methodology relies on a multi-observation approach, consisting in combining multiple independent measurements into a single dataset, with the aim of over-determining the problem. In the present work, a poroelastic sample is placed in an impedance tube and tested in two loading conditions, namely in a rigid-backing configuration and coupled to a resonant expansion chamber. Given the non-monotonic nature of the experimental data, an incremental parameter estimation procedure is used in order to guide the model parameters towards the global solution without terminating at local minima. A statistical inversion approach is also discussed, providing refined point estimates, uncertainty ranges and parameter correlations. The methodology is applied to the characterisation of a sample of melamine foam and provides estimates of all nine parameters with compact uncertainty ranges. It is shown that the model parameters are retrieved with a lower uncertainty in the multi-observation case, as compared with a single-observation case. The method proposed here does not require prior knowledge of the thickness or any of the properties of the sample, and can be carried out with a standard two-microphone impedance tube.

Acoustic measurement and statistical characterization of direct-printed, variable-porosity aluminum foams.

Additive manufacturing has expanded greatly in recent years with the promise of being able to create complex and custom structures at will. Enhanced control over the microstructure properties, such as percent porosity, is valuable to the acoustic design of materials. In this work, aluminum foams are fabricated using a modified powder bed fusion method, which enables voxel-by-voxel printing of structures ranging from fully dense to approximately 50% porosity. To understand the acoustic response, samples are measured in an acoustic impedance tube and characterized with the Johnson-Champoux-Allard-Lafarge model for rigid-frame foams. Bayesian statistical inversion of the model parameters is performed to assess the applicability of commonly employed measurement and modeling methods for traditional foams to the additively manufactured, low porosity aluminum foams. This preliminary characterization provides insights into how emerging voxel-by-voxel additive manufacturing approaches could be used to fabricate acoustic metal foams and what could be learned about the microstructure using traditional measurement and analysis techniques.

Uncertainty quantification of in situ horizontal stress with pressuremeter using a statistical inverse analysis method

Knowledge of in situ stress magnitude and orientation plays a very important role in geological/geotechnical engineering and in the development of energy resources, such as caprock integrity, waste fluid disposal, geological storage of CO2, and geothermal energy extraction. The uncertainty of estimated parameters, especially horizontal stress, from in situ tests such as pressuremeter tests is a long-standing challenge owing to the existence of uncertainties from geomaterial spatial variability, measurement errors, limited information, and modelling methods. Therefore, non-unique solutions are often encountered in pressuremeter interpretation. In this study, a statistical inverse analysis method is proposed to solve this issue by combining a closed-form solution, finite-difference model, and selected optimization algorithms. The objective of the statistical inverse analysis is to determine the optimal parameters by minimizing the sum of squared errors while providing the confidence intervals of inversed parameters. Random variables generated in the optimization process reproduce the potential parameter uncertainties. The Jacobian matrix and confidence intervals are derived from the optimization process to evaluate variability of the predicted horizontal stress and ground properties. A workflow is presented that demonstrates a statistical inverse method for analyzing pressuremeter results and helps quantify uncertainties of the ground properties and in situ stress magnitudes and orientations derived from a pressuremeter test.

Investigation of precision, accuracy and confidence of X-ray diffraction for determining crystallite size in nanopowders

X-ray diffraction (XRD) is often utilized as a method of determining bulk sample crystallite size in powder characterization. While it is generally accepted that XRD peak broadening allows for qualitative crystallite size comparisons, its use for quantitative information is still debated. This study investigates the quantitative capability of XRD for determining the crystallite sizes of magnesium oxide nanocrystals by examining the precision, accuracy and uncertainty using the whole pattern (WP) weighted least-squares and Williamson–Hall (WH) methods. The precision of the methods was investigated by re-preparing, re-running and re-analysing identical samples. Both methods were found to be precise within 2 nm. The accuracy of the methods was investigated by comparing them against independent crystallite size analyses using visual particle identification from scanning electron microscopy micrographs and from indirect calculations using Brunauer–Emmett–Teller (BET) adsorption-determined surface areas. The WP method was found to be more accurate than the WH method, which consistently underpredicted the crystallite size. Finally, the confidence of the methods was investigated using a Bayesian inference statistical inversion method. The WP method was found to have a narrower confidence distribution in its crystallite size determination than the WH method. The broad WH confidence indicates that reliable quantitative single-measurement crystallite size determinations are not feasible using the WH technique. However, the WP method demonstrated precision, accuracy and confidence, allowing quantitative crystallite size determinations to be made.

Modeling extra-deep electromagnetic logs using a deep neural network

Modern geosteering is heavily dependent on real-time interpretation of deep electromagnetic (EM) measurements. We have developed a methodology to construct a deep neural network (DNN) model trained to reproduce a full set of extra-deep EM logs consisting of 22 measurements per logging position. The model is trained in a 1D layered environment consisting of up to seven layers with different resistivity values. A commercial simulator provided by a tool vendor is used to generate a training data set. The data set size is limited because the simulator provided by the vendor is optimized for sequential execution. Therefore, we design a training data set that embraces the geologic rules and geosteering specifics supported by the forward model. We use this data set to produce an EM simulator based on a DNN without access to the proprietary information about the EM tool configuration or the original simulator source code. Despite using a relatively small training set size, the resulting DNN forward model is quite accurate for the considered examples: a multilayer synthetic case and a section of a published historical operation from the Goliat field. The observed average evaluation time of 0.15 ms per logging position makes it also suitable for future use as part of evaluation-hungry statistical and/or Monte Carlo inversion algorithms within geosteering workflows.

Retrieval of Oceanic Total Precipitable Water Vapor and Cloud Liquid Water from Fengyun-3D Microwave Sounding Instruments

Fengyun-3D (FY-3D) satellite is the latest polar-orbiting meteorological satellite launched by China and carries 10 instruments onboard. Its microwave temperature sounder (MWTS) and microwave humidity sounder (MWHS) can acquire a total of 28 channels of brightness temperatures, providing rich information for profiling atmospheric temperature and moisture. However, due to a lack of two important frequencies at 23.8 and 31.4 GHz, it is difficult to retrieve the total precipitable water vapor (TPW) and cloud liquid water path (CLW) from FY-3D microwave sounder data as commonly done for other microwave sounding instruments. Using the channel similarity between Suomi National Polar-orbiting Partnership (NPP) advanced technology microwave sounder (ATMS) and FY-3D microwave sounding instruments, a machine learning (ML) technique is used to generate the two missing low-frequency channels of MWTS and MWHS. Then, a new dataset named as combined microwave sounder (CMWS) is obtained, which has the same channel setting as ATMS but the spatial resolution is consistent with MWTS. A statistical inversion method is adopted to retrieve TPW and CLW over oceans from the FY-3D CMWS. The intercomparison between different satellites shows that the inversion products of FY-3D CMWS and Suomi NPP ATMS have good consistency in magnitude and distribution. The correlation coefficients of retrieved TPW and CLW between CMWS and ATMS can reach 0.95 and 0.85, respectively.