Abstract

Abstract

In this work we discuss a variational approach for the determination of the parameters of systems of ordinary differential equations (ODE). We construct a model for fitting observed noisy data into the given dynamical system. Also we explain in detail the advantage of using the adjoint equation method to compute the derivatives or gradients, which are needed for the application of gradient methods and quasi-Newton algorithms to find the minimum of the cost function. In particular we consider two classic iterative algorithms: the conjugate gradient (CG) algorithm and the BFGS algorithm. For educational purposes we try to explain several numerical and computational issues with some detail and illustrate them with the SEIRD epidemiological model.

Abstract

The conceptual simplicity and the ability of cohesive finite element models to describe complex fracture phenomena makes them often the approach of choice to study dynamic fracture. These models have proven to reproduce some experimental features, but to this point, no systematic study has validated their predictive ability; the difficulty in producing a sufficiently complete experimental record, and the intensive computational requirements needed to obtain converged simulations are possible causes. Here, we present a systematic integrated numerical–experimental approach to the verification and validation (V&V) of simulations of dynamic fracture along weak planes. We describe the intertwined computational and the experimental sides of the work, present the V&V results, and extract general conclusions about this kind of integrative approach.

Abstract

Guided wave-based Structural Health Monitoring (SHM) tools utilize the guided wave responses to interrogate damage in structures. This research demonstrates the use of various objective functions in single (mono) objective and multi-objective genetic algorithms for damage identification in isotropic 1D structures. The time domain spectral element method and a deep-learning-based surrogate is utilized for simulating wave propagation in an isotropic cracked rod. The genetic algorithms employ results ('numerical experiment') obtained from the spectral element model and the deep-learning-based surrogate to determine the optimized crack locations and crack depths as output parameters. The obtained optimized parameters from genetic algorithms are compared in terms of errors for various objective functions.

Abstract