Timo Lähivaara

Bayesian Approach to Tree Detection Based on Airborne Laser Scanning Data

In this paper, we consider a computational method for detecting trees on the basis of airborne laser scanning (ALS) data. In the approach, locations, heights, and crown shapes of trees are tracked automatically by fitting multiple 3-D crown height models to ALS data of a field plot. The estimates are computed with an iterative reconstruction method based on Bayesian inversion paradigm. The formulation allows for utilizing prior information on tree shapes in the estimation. Here, the prior models are written based on field measurement data and allometric models for tree shapes. The feasibility of the approach is tested with ALS and field data from a managed boreal forest. The algorithm found 70.2% of the trees in the area, which is a clear improvement compared to a usual 2.5D crown delineation approach (53.1% of the trees detected).

COMPUTATIONAL ASPECTS OF THE DISCONTINUOUS GALERKIN METHOD FOR THE WAVE EQUATION

The Discontinuous Galerkin (DG) method is a powerful tool for numerically simulating wave propagation problems. In this paper, the time-dependent wave equation is solved using the DG method for spatial discretization; and the Crank–Nicolson and fourth-order explicit, singly diagonally implicit Runge–Kutta methods, and, for reference, the explicit Runge–Kutta method, were used for time integration. These simulation methods were studied using two-dimensional numerical experiments. The aim of the experiments was to study the effect of the polynomial degree of the basis functions, grid density, and the Courant–Friedrichs–Lewy number on the accuracy of the approximation. The sensitivity of the methods to distorted finite elements was also examined. Results from the DG method were compared with those computed using a conventional finite element method. Three different model problems were considered. In the first experiment, wave propagation in a homogeneous medium was studied. In the second experiment, the scattering and propagation of waves in an inhomogeneous medium were investigated. The third experiment evaluated wave propagation in a more complicated domain involving multiple scattering waves. The results indicated that the DG method provides more accurate solutions than the conventional finite element method with a reduced computation time and a lower number of degrees of freedom.

Estimation of aquifer dimensions from passive seismic signals with approximate wave propagation models

Recently, it has been proposed that spontaneous seismic activity could be used in the estimation of hydrological parameters of aquifers such as permeability and storage. Approximate wave propagation models such as ray tracing, which are commonly used in hydrological parameter estimation with active sources and backscattering geometry, are not feasible with passive seismological imaging. With respect to full wave propagation models, the most accurate known model for aquifers is the poroelastic model while bedrock is usually modelled as an elastic medium. Using a poroelastic model in the forward model can be a computationally impractical choice. In this paper, we carry out a feasibility study in which we attempt to estimate the aquifer depth and water table using a highly approximate elastic model also for the aquifer. We adopt the Bayesian approximation error approach in which a statistical model is constructed for the errors that are induced by using model approximations such as sparse meshing and simplified physical models. We consider the problem in a simple two-dimensional geometry and show that straightforward adoption of approximate models leads to inconsistent parameter estimates, that is, the true parameters have essentially vanishing posterior density. On the other hand, using the Bayesian approximation error approach, the parameter estimates are consistent.

A non-uniform basis order for the discontinuous Galerkin method of the 3D dissipative wave equation with perfectly matched layer

In this study a discontinuous Galerkin method (DG) for solving the three-dimensional time-dependent dissipative wave equation is investigated. In the case of unbounded problems, the perfectly matching layer (PML) is used to truncate the computational domain. The aim of this work is to investigate a simple selection method for choosing the basis order for elements in the computational mesh in order to obtain a predetermined error level. The selection method studied here relies on the error estimates provided by Ainsworth [M. Ainsworth, Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods, Journal of Computational Physics 198(1) (2004) 106-130]. The performance of the non-uniform basis is examined using numerical experiments. In the simulated model problems, a feasible method choosing the basis order for arbitrary sized elements is achieved. In simulations, the effect of dissipation and the choices of the PML parameters on the performance of the DG method are also investigated.

Uncertainty Quantification in ALS-Based Species-Specific Growing Stock Volume Estimation

In this paper, we propose an approach to quantify the plot-level uncertainty in species-specific growing stock volume estimated from airborne laser scanning data and aerial imagery. This is accomplished by adopting the framework of Bayesian inference in the area-based estimation of stock volume. The results show that the proposed approach performs well in quantifying the estimate uncertainty and produces optimal interval estimates for species-specific volumes when sufficient training data are available. Also the point estimate accuracy is competitive with current state-of-the-art methods. Furthermore, we demonstrate how the quantified uncertainties of the stand attributes can be utilized to determine the uncertainty in classification done using the estimated stand attributes.

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

The feasibility of data based machine learning applied to ultrasound tomography is studied 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, a high-order discontinuous Galerkin method is considered, while deep convolutional neural networks are used to solve the parameter estimation problem. In the numerical experiment, the material porosity and tortuosity is estimated, while the remaining parameters which are of less interest are successfully marginalized in the neural networks-based inversion. Computational examples confirm the feasibility and accuracy of this approach.

Estimating pipeline location using ground-penetrating radar data in the presence of model uncertainties

We study the inverse problem of estimating the pipeline location from ground-penetrating radar data in the context of Bayesian inversion. Maxwell?s equations are used to model the electromagnetic wave propagation, and are solved using a high-order discontinuous Galerkin method. The uncertainties related to the wave propagation in inhomogeneous background are taken into account by the Bayesian approximation error (BAE) approach. The inverse problem is solved using the full waveform data. Numerical simulations suggest that by using the BAE the model uncertainties can be taken satisfactorily into account, while at the same time making a significant reduction in the computational burden. Furthermore, the estimates for the location of the pipeline are feasible in the sense that the posterior model supports the actual location.

Bayesian approach to tree detection with airborne laser scanning

In this paper, we propose a novel computational approach to tree detection. The aim is to reconstruct the positions, sizes and crown shapes of trees. This amounts to simultaneous tree localization and estimation of tree shapes by fitting multiple CHMs to ALS data. This estimation problem is written in Bayesian inversion framework. The benefit of the Bayesian approach is that it enables accounting for statistical prior information on the unknown parameters in the estimation. The prior information is explicitely written in the form of a probability distribution that models the unknowns. Here, the prior information is associated with the statistics of tree height, crown height and crown width. We hypothesize that utilizing such information in the estimation improves the detection of trees in dense forests, i.e. cases where the existing reconstruction methods usually fail. The feasibility of the proposed approach is tested with ALS data. The estimates are compared with field measurements. The preliminary results demonstrate that the positions and sizes of the trees can be tracked relatively well, even if tree crowns are interlaced.

Audio acoustic modeling using full‐wave methods

The numerical simulation of wave propagation poses a significant challenge in scientific computation. Historically, several approaches are explored in order to get a stable method that can be efficiently used for approximating wave propagation without excessive numerical dissipation or dispersion. Unfortunately, the traditional approaches, such as the finite element and the finite difference, require many discretization points per wavelength to obtain reliable solutions. In this study, two alternative full‐wave methods for reducing the computational complexity are consider. The methods are the time‐domain discontinuous Galerkin method and the ultraweak variational formulation in the frequency domain. Using these techniques, the directivity and the frequency response of a loudspeaker are studied. Moreover, the simulated results are compared to experimental measurements.

Deterministic and statistical parameter characterization in resonant fluid-structure interaction problems

This research focuses on developing computational methods to estimate model parameters in resonant fluid-structure interaction problems over a wide frequency range by means of model inversion approaches. The considered problems are widely known to be subjected to local minima, which represent a major challenge in the field of parameter identification. In the proposed method, the frequency spectrum is divided into successive substeps allowing to efficiently guide the estimation towards the global minimum, i.e., the true model parameters. The estimation is performed through two frameworks, namely, the deterministic using gradient-based optimization and Bayesian using Markov chain Monte Carlo method. Proposed numerical examples illustrate the effectiveness and potential of the proposed stepwise scheme to find the global minimum and reduce the overall computational burden.This research focuses on developing computational methods to estimate model parameters in resonant fluid-structure interaction problems over a wide frequency range by means of model inversion approaches. The considered problems are widely known to be subjected to local minima, which represent a major challenge in the field of parameter identification. In the proposed method, the frequency spectrum is divided into successive substeps allowing to efficiently guide the estimation towards the global minimum, i.e., the true model parameters. The estimation is performed through two frameworks, namely, the deterministic using gradient-based optimization and Bayesian using Markov chain Monte Carlo method. Proposed numerical examples illustrate the effectiveness and potential of the proposed stepwise scheme to find the global minimum and reduce the overall computational burden.