Statistical Inversion Approach Research Articles

Dynamic water vapor sorption in wood-based fibrous materials and material parameter estimation

Building physical simulation software rely on assumptions regarding the local equilibria in materials’ pore systems, which may be unjustified for certain materials. While local hygrothermal non-equilibrium has still been in focus in some previous studies, it has been unclear how significant factor it may be when modeling real structures. In case of wood, the non-equilibrium is related to the slowness of intrusion of water molecules into the hygroscopic cell walls. Including local non-equilibrium in macroscopic model requires separate variables for pore air vapor and adsorbed moisture, and modeling the local mass transfer between pore air and adsorbed moisture requires effective material parameters, whose experimental determination is not straightforward. Commercially available sorption balances can be used to record data, which can be used in the parameter estimation. In this type of problem of parameter estimation from time-dependent data the mathematical challenge is to find global optimum from different solutions, which yield similar values for objective function. This difficulty can be overcome by using statistical inversion approach, which we applied in studying low-density woodfibre material (LDF). Dynamic sorption parameters were finally applied in numerical analysis of a laboratory test assembly. Based on the results, our conclusion is that the slowness of sorption is obvious in small LDF sample, which is exposed to changing humidity, but with the studied material the sorption seem to happen fast enough so that local non-equilibrium may have only slight effects in modeling of real structures.

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.

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.

Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method

The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthal resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this paper, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.

Structural damage identification via time domain response and Markov Chain Monte Carlo method

The present work addresses the problem of structural damage identification built on the statistical inversion approach. Here, the damage state of the structure is continuously described by a cohesion parameter, which is spatially discretized by the finite element method. The inverse problem of damage identification is then posed as the determination of the posterior probability densities of the nodal cohesion parameters. The Markov Chain Monte Carlo method, implemented with the Metropolis–Hastings algorithm, is considered in order to approximate the posterior probabilities by drawing samples from the desired joint posterior probability density function. With this approach, prior information on the sought parameters can be used and the uncertainty concerning the known values of the material properties can be quantified in the estimation of the cohesion parameters. The assessment of the proposed approach has been performed by means of numerical simulations on a simply supported Euler–Bernoulli beam. The damage identification and assessment are performed considering time domain response data. Different damage scenarios and noise levels were addressed, demonstrating the feasibility of the proposed approach.

Sparse source travel-time tomography of a laboratory target: accuracy and robustness of anomaly detection

This study concerned conebeam travel-time tomography. The focus was on a sparse distribution of signal sources that can be necessary in a challenging in situ environment such as in asteroid tomography. The goal was to approximate the minimum number of source positions needed for robust detection of refractive anomalies, e.g., voids within an asteroid or a casting defects in concrete. Experimental ultrasonic data were recorded utilizing as a target a 150 mm plastic cast cube containing three stones with diameter between 22 and 41 mm. A signal frequency of 55 kHz (35 mm wavelength) was used. Source counts from one to six were tested for different placements. Based on our statistical inversion approach and analysis of the results, three or four sources were found to lead to reliable inversion. The source configurations investigated were also ranked according to their performance. Our results can be used, for example, in the planning of planetary missions as well as in material testing.

Statistical inversion approach to estimating water content in an aquifer from seismic data

This study focuses on developing computational tools to estimate water content in an aquifer from seismic measurements. The poroelastic signature from an aquifer is simulated and methods that use this signature to estimate the water table level and aquifer thickness are investigated. In this work, the spectral-element method is used to solve the forward model that characterizes the propagation of seismic waves. The inverse problem is formulated in the Bayesian framework, so that all uncertainties are explicitly modelled as probability distributions, and the solution is given as summary statistics over the posterior distribution of parameters relative to data. For the inverse problem, we use the Bayesian approximation error method which reduces the overall computational demand. In this study, results in the two-dimensional case with simulated data are presented.

A statistical inversion approach for local thermal diffusivity and heat flux simultaneous estimation

The mapping of thermophysical properties from thermal images provided by an infrared camera is a difficult inverse problem, due to the large amount of data to be processed, large number of parameters to be estimated and low signal-to-noise ratio. It is thus of great interest to implement estimation approaches of low computational cost that can accurately cope with such inherent difficulties. In this paper, we make use of the so-called statistical inversion approach for the solution of an inverse problem that involves the identification of both local thermal diffusivity and local heat flux. Experimental results are presented for two kinds of heating: front face heating with a laser diode and back surface heating with an electrical resistance.

Model reduction and pollution source identification from remote sensing data

We consider a source identification problem related to determination of contaminant source parameters in lake environments using remote sensing measurements. We carry out a numerical example case study in which we employ the statistical inversion approach for the determination of the source parameters. In the simulation study a pipeline breaks on the bottom of a lake and only low-resolution remote sensing measurements are available. We also describe how model uncertainties and especially errors that are related to model reduction are taken into account in the overall statistical model of the system. The results indicate that the estimates may be heavily misleading if the statistics of the model errors are not taken into account.

An efficient deconvolution algorithm for estimating oxygen consumption during muscle activities

The reconstruction of an unknown input function from noisy measurements in a biological system is an ill-posed inverse problem. Any computational algorithm for its solution must use some kind of regularization technique to neutralize the disastrous effects of amplified noise components on the computed solution. In this paper, following a hierarchical Bayesian statistical inversion approach, we seek estimates for the input function and regularization parameter (hyperparameter) that maximize the posterior probability density function. We solve the maximization problem simultaneously for all unknowns, hyperparameter included, by a suitably chosen quasi-Newton method. The optimization approach is compared to the sampling-based Bayesian approach. We demonstrate the efficiency and robustness of the deconvolution algorithm by applying it to reconstructing the time courses of mitochondrial oxygen consumption during muscle state transitions ( e.g., from resting state to contraction and recovery), from the simulated noisy output of oxygen concentration dynamics on the muscle surface. The model of oxygen transport and metabolism in skeletal muscle assumes an in vitro cylindrical structure of the muscle in which the oxygen from the surrounding oxygenated solution diffuses into the muscle and is then consumed by the muscle mitochondria. The algorithm can be applied to other deconvolution problems by suitably replacing the forward model of the system.

Statistical inversion of South Atlantic circulation in an abyssal neutral density layer

This paper introduces a Bayesian inversion approach to estimating steady state ocean circulation and tracer fields. It is based on a quasi-horizontal flow model and a PDE solver for the forward problem of computing solutions to the tracer field advection-diffusion equations. A typical feature of existing ocean circulation inverse methods is a preprocessing stage in which the tracer data are interpolated over a regular grid and the interpolation error is ignored in the subsequent inversion. Our approach only uses interpolated data at those grid points that have neighboring hydrographic stations. By exploiting physically-based models in an integrated fashion, the method provides a statistically unified inversion and tracer field reconstruction with minimal data smoothing. Solving the problem consists of finding information about the circulation and tracer fields in the presence of a number of assumptions (prior information); the resulting posterior probability distribution summarizes what we can know about these fields. We develop a Markov chain Monte Carlo simulation procedure to extract information from the (analytically intractable) posterior distribution of all the parameters in the model; uncertainty about the “solution” is represented by variation in the output of the simulation runs. Our approach is aimed at finding the time-averaged quasi-horizontal flow and tracer fields for an abyssal neutral density layer in the South Atlantic. The collection of oceanographic data during the past century has formed the basis for our understanding of the distribution of properties and the circulation in the ocean. However, a description of the steady flow and associated property fields in the oceanic interior that is dynamically consistent with those collective observations and that accounts for the inherent uncertainty associated with measurements, physical variability and model parameterizations, for example, is still lacking. It may be that the steady-state assumption is a poor approximation to the equations of motion, but this hypothesis deserves close attention as a test of our understanding of the basic physics of the ocean circulation. In this paper we introduce a physically-based statistical inversion approach to estimate the

A robust statistical-based estimator for soil moisture retrieval from radar measurements

The authors examine the use of a robust statistical inversion approach to the estimation of soil moisture and roughness statistics from backscatter measurements. Two sets of basis functions are examined; the first is a set of basis functions from multinomial combinations of the inputs (termed the MBF) while the second is a set of basis functions generated by a multilayer perceptron referred to as MLPBF. The authors discuss potential sources of training patterns upon which to base these estimators, including empirical forward models and more rigorous theoretical scattering models such as the IEM. These estimators are applied to a set of measured POLARSCAT data from Oh et al. [1992]. Comparisons are made with other inversion methods including neural networks.

Development of geophysical retrieval algorithms for the MIMR

The feasibility of using spaceborne microwave radiometry to retrieve geophysical parameters is described. The study concentrates on the development of inversion techniques for multichannel spaceborne radiometers, especially the statistical inversion approach. The applications of the planned MIMR (Multi-Frequency Imaging Microwave Radiometer) instrument are discussed. The inversion algorithms used are conventional algorithms for different applications and the statistical inversion approach. Comparisons between results from different inversion algorithms are presented. The statistical inversion approach has been found to give promising parameter retrieval accuracies and has the potential to improve the operational use of passive spaceborne remote sensing. An analysis of the sensitivity of the radiometer apparent temperature to different geophysical parameters and the statistical behavior of the atmospheric transmissivity are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>