Characterising poroelastic materials in the ultrasonic range - A Bayesian approach

Acoustic fields scattered by poroelastic materials contain key information about the materials' pore structure and elastic properties. Therefore, such materials are often characterised with inverse methods that use acoustic measurements. However, it has been shown that results from many existing inverse characterisation methods agree poorly. One reason is that inverse methods are typically sensitive to even small uncertainties in a measurement setup, but these uncertainties are difficult to model and hence often neglected. In this paper, we study characterising poroelastic materials in the Bayesian framework, where measurement uncertainties can be taken into account, and which allows us to quantify uncertainty in the results. Using the finite element method, we simulate measurements where ultrasonic waves are incident on a water-saturated poroelastic material in normal and oblique angles. We consider uncertainties in the incidence angle and level of measurement noise, and then explore the solution of the Bayesian inverse problem, the posterior density, with an adaptive parallel tempering Markov chain Monte Carlo algorithm. Results show that both the elastic and pore structure parameters can be feasibly estimated from ultrasonic measurements.Comment: Published in JSV. https://doi.org/10.1016/j.jsv.2019.05.02

Deep convolutional neural networks for estimating porous material parameters with ultrasound tomography

We study the feasibility of data based machine learning applied to ultrasound tomography to estimate water-saturated porous material parameters. In this work, the data to train the neural networks is simulated by solving wave propagation in coupled poroviscoelastic-viscoelastic-acoustic media. As the forward model, we consider a high-order discontinuous Galerkin method while deep convolutional neural networks are used to solve the parameter estimation problem. In the numerical experiment, we estimate the material porosity and tortuosity while the remaining parameters which are of less interest are successfully marginalized in the neural networks-based inversion. Computational examples confirms the feasibility and accuracy of this approach

A High-Order Ultra-Weak Variational Formulation for Electromagnetic Waves Utilizing Curved Elements

The Ultra Weak Variational Formulation (UWVF) is a special Trefftz discontinuous Galerkin method, here applied to the time-harmonic Maxwell's equations. The method uses superpositions of plane waves to represent solutions element by element on a finite element mesh. We discuss the use of our parallel UWVF implementation called ParMax, and concentrate on methods for obtaining high order solutions in the presence of scatterers with piecewise smooth boundaries. In particular, we show how curved surface triangles can be incorporated in the UWVF. This requires quadrature to assemble the system matrices. We also show how to implement a total field and scattered field approach, together with the transmission conditions across an interface to handle resistive sheets. We note also that a wide variety of element shapes can be used, that the elements can be large compared to the wavelength of the radiation, and that a matrix free version is easy to implement (although computationally costly). Our contributions are illustrated by several numerical examples showing that curved elements can improve the efficiency of the UWVF, and that the method accurately handles resistive screens as well as PEC and penetrable scatterers. Using large curved elements and the matrix free approach, we are able to simulate scattering from an aircraft at X-band frequencies. The innovations here demonstrate the applicability of the UWVF for industrial examples

Tomography-assisted control for the microwave drying process of polymer foams

This paper presents the integration of electrical capacitance tomography (ECT) with a moisture controller for the microwave drying of polymer foam. The proportional–integral (PI) control and the linear quadratic Gaussian (LQG) control are employed in designing the controller. The control objective in this process is that the moisture of polymer foam after the drying process reaches the desired set point. The permittivity distribution of polymer foam after the drying process is estimated in real-time using a designed ECT sensor and transferred as feedback to the controller. Since the permittivity and the moisture are strongly correlated, the material moisture can be controlled by controlling the permittivity. A state-space model is derived for the microwave drying process based on a system identification approach using the experimental data from the process. The derived model is employed in designing the LQG controller and adjusting the parameters of the PI controller. The designed controllers are implemented on a testbed microwave oven, and the experimental results show that the designed controllers are able to follow the desired set point moisture. The performance of the system with both controllers is compared, and their advantages and disadvantages are discussed. Moreover, the benefits of having a moisture controller for the microwave drying process are shown in simulation studies compared to an uncontrolled system

An electromagnetic time-reversal imaging algorithm for moisture detection in polymer foam in an industrial microwave drying system

Microwave tomography (MWT) based control is a novel idea in industrial heating systems for drying polymer foam. In this work, an X-band MWT module is designed and developed using a fixed antenna array configuration and integrated with the HEPHAISTOS industrial heating system. A decomposition of the time-reversal operator (DORT) algorithm with a proper Green’s function of multilayered media is utilized to localize the moisture location. The derived Green’s function can be applied to the media with low or high contrast layers. It is shown that the time-reversal imaging (TRI) with the proposed Green’s function can be applied to the multilayered media with a moderately rough surface. Moreover, a single frequency TRI is proposed to decrease the measurement time. Numerical results for different moisture scenarios are presented to demonstrate the efficacy of the proposed method. The developed method is then tested on the experimental data for different moisture scenarios from our developed MWT experimental prototype. Image reconstruction results show promising capabilities of the TRI algorithm in estimating the moisture location in the polymer foam

Monitoring of water content in a porous reservoir by seismic data: A 3D simulation study

A potential framework to estimate the amount of water stored in a porous storage reservoir from seismic data is neural networks. In this study, the water storage reservoir system is modeled as a coupled poroviscoelastic-viscoelastic medium, and the underlying wave propagation problem is solved using a three-dimensional discontinuous Galerkin method coupled with an Adams-Bashforth time stepping scheme. The wave problem solver is used to generate databases for the neural network-based machine learning model to estimate the water content. In the numerical examples, we investigate a deconvolution-based approach to normalize the effect from the source wavelet in addition to the network's tolerance for noise levels. We also apply the SHapley Additive exPlanations method to obtain greater insight into which part of the input data contributes the most to the water content estimation. The numerical results demonstrate the capacity of the fully connected neural network to estimate the amount of water stored in the porous storage reservoir