5 research outputs found
Immersed boundary parametrizations for full waveform inversion
Full Waveform Inversion (FWI) is a successful and well-established inverse
method for reconstructing material models from measured wave signals. In the
field of seismic exploration, FWI has proven particularly successful in the
reconstruction of smoothly varying material deviations. In contrast,
non-destructive testing (NDT) often requires the detection and specification of
sharp defects in a specimen. If the contrast between materials is low, FWI can
be successfully applied to these problems as well. However, so far the method
is not fully suitable to image defects such as voids, which are characterized
by a high contrast in the material parameters. In this paper, we introduce a
dimensionless scaling function to model voids in the forward and
inverse scalar wave equation problem. Depending on which material parameters
this function scales, different modeling approaches are presented,
leading to three formulations of mono-parameter FWI and one formulation of
two-parameter FWI. The resulting problems are solved by first-order
optimization, where the gradient is computed by an ajdoint state method. The
corresponding Fr\'echet kernels are derived for each approach and the
associated minimization is performed using an L-BFGS algorithm. A comparison
between the different approaches shows that scaling the density with
is most promising for parameterizing voids in the forward and inverse problem.
Finally, in order to consider arbitrary complex geometries known a priori, this
approach is combined with an immersed boundary method, the finite cell method
(FCM).Comment: 23 pages, 21 figure
On the Use of Neural Networks for Full Waveform Inversion
Neural networks have recently gained attention in solving inverse problems.
One prominent methodology are Physics-Informed Neural Networks (PINNs) which
can solve both forward and inverse problems. In the paper at hand, full
waveform inversion is the considered inverse problem. The performance of PINNs
is compared against classical adjoint optimization, focusing on three key
aspects: the forward-solver, the neural network Ansatz for the inverse field,
and the sensitivity computation for the gradient-based minimization. Starting
from PINNs, each of these key aspects is adapted individually until the
classical adjoint optimization emerges. It is shown that it is beneficial to
use the neural network only for the discretization of the unknown material
field, where the neural network produces reconstructions without oscillatory
artifacts as typically encountered in classical full waveform inversion
approaches. Due to this finding, a hybrid approach is proposed. It exploits
both the efficient gradient computation with the continuous adjoint method as
well as the neural network Ansatz for the unknown material field. This new
hybrid approach outperforms Physics-Informed Neural Networks and the classical
adjoint optimization in settings of two and three-dimensional examples
Implicit-Explicit Time Integration for the Immersed Wave Equation
Immersed boundary methods simplify mesh generation by embedding the domain of
interest into an extended domain that is easy to mesh, introducing the
challenge of dealing with cells that intersect the domain boundary. Combined
with explicit time integration schemes, the finite cell method introduces a
lower bound for the critical time step size. Explicit transient analyses
commonly use the spectral element method due to its natural way of obtaining
diagonal mass matrices through nodal lumping. Its combination with the finite
cell method is called the spectral cell method. Unfortunately, a direct
application of nodal lumping in the spectral cell method is impossible due to
the special quadrature necessary to treat the discontinuous integrand inside
the cut cells. We analyze an implicit-explicit (IMEX) time integration method
to exploit the advantages of the nodal lumping scheme for uncut cells on one
side and the unconditional stability of implicit time integration schemes for
cut cells on the other. In this hybrid, immersed Newmark IMEX approach, we use
explicit second-order central differences to integrate the uncut degrees of
freedom that lead to a diagonal block in the mass matrix and an implicit
trapezoidal Newmark method to integrate the remaining degrees of freedom (those
supported by at least one cut cell). The immersed Newmark IMEX approach
preserves the high-order convergence rates and the geometric flexibility of the
finite cell method. We analyze a simple system of spring-coupled masses to
highlight some of the essential characteristics of Newmark IMEX time
integration. We then solve the scalar wave equation on two- and
three-dimensional examples with significant geometric complexity to show that
our approach is more efficient than state-of-the-art time integration schemes
when comparing accuracy and runtime
Eco-Driving for Different Electric Powertrain Topologies Considering Motor Efficiency
Electrification and automatization may change the environmental impact of vehicles. Current eco-driving approaches for electric vehicles fit the electric power of the motor by quadratic functions and are limited to powertrains with one motor and single-speed transmission or use computationally expensive algorithms. This paper proposes an online nonlinear algorithm, which handles the non-convex power demand of electric motors. Therefore, this algorithm allows the simultaneous optimization of speed profile and powertrain operation for electric vehicles with multiple motors and multiple gears. We compare different powertrain topologies in a free-flow scenario and a car-following scenario. Dynamic Programming validates the proposed algorithm. Optimal speed profiles alter for different powertrain topologies. Powertrains with multiple gears and motors require less energy during eco-driving. Furthermore, the powertrain-dependent correlations between jerk restriction and energy consumption are shown