86,780 research outputs found
State, parameters and hidden dynamics estimation with the Deep Kalman Filter: Regularization strategies
No full textIn this paper we present in detail the various regularization strategies adopted for a novel scientific machine learning extension of the well known Kalman Filter (KF) that we call the Deep Kalman Filter (DKF), briefly presented in the conference paper (Chinellato and Marcuzzi 2024) . It is based on a recent scientific machine learning paradigm, called algorithm unfolding/unrolling, that allows to create a neural network from the algebraic structure dictated by an analytical method of scientific computing. We show the interpretable consistency of DKF with the classic KF when this is optimal, and its improvements against the KF with both linear and nonlinear models in general. Indeed, the DKF learns parameters of a quite general reference model, comprising: corrector gains, predictor model parameters and eventual unmodeled dynamics. This goes well beyond the ability of the KF and its known extensions
A Numerical Feed-Forward Scheme for the Augmented Kalman Filter
No full textIn this paper we present a numerical feed-forward strategy for the Augmented Kalman Filter and show its application to a diffusion-dominated inverse problem: heat source reconstruction from boundary measurements. The method is applicable in general to forcing term estimation in lumped and distributed parameters models and gives a significant contribution where, in industry and science, probing signals are used through a diffusive material-body to estimate its localized internal properties in a non-destructive test, like in ultrasound or thermographic inspection
Accurate detection of hidden material changes as fictitious heat sources
No full textIn this article we present a numerical method for the estimation of hidden material changes, interpreted as fictitious source terms. The method adapts the parameters of its reference model in order to cancel the estimated fictitious source terms and thus it indirectly estimates the hidden material changes. The novelty of this method is triple: first, a parsimonious minimization strategy that effectively avoids local minima, by using the maximum principle as a barrier against falling into; second, an error indicator based on estimates of fictitious heat sources, instead of the temperatures-prediction-error, because it is smeared by diffusion; third, the adaptation of model parameters is computed without the problematic matrix inversion which would arise in Newton-based procedures. As a particular example application, we show that, in thermographic experiments for hidden corrosion detection, the gradient of the temperatures-prediction-error, often used in the literature, is quite inefficient, while the fictitious-source-term estimation behaves intrinsically better. Its accuracy and moderate computational demand are highlighted in the numerical tests. Moreover, this approach is applicable to general hidden material change problems
Hit detection in audio mixtures by means of a physics-aware Deep-NMF algorithm
No full textIn this paper we present the Physics-Aware Deep-NMF (PAD-NMF) algorithm and we apply it to hit detection in mechanical systems from audio mixtures. The algorithm accurately extracts the acoustic emission made by the physical source to be monitored, to be properly used in engineering analysis, like e.g. the hit detection here considered. This is mainly a source separation problem where sources have a precise physical meaning, that should be retained by the processing algorithm. For this reason we call this algorithm a Physics-aware soft-sensor. We give a detailed description of the algorithm and show its results on a general application with critical signal-to-noise ratios, where the noise is a mixture of random and deterministic acoustic sources
State Estimation of Partially Unknown Dynamical Systems with a Deep Kalman Filter
No full textIn this paper we present a novel scientific machine learning reinterpretation of the well-known Kalman Filter, we explain its flexibility in dealing with partially-unknown models and show its effectiveness in a couple of situations where the classic Kalman Filter is problematic
Deviation maximization for rank-revealing QR factorizations
No full textIn this paper, we introduce a new column selection strategy, named here “Deviation Maximization”, and apply it to compute rank-revealing QR factorizations as an alternative to the well-known block version of the QR factorization with the column pivoting method, called QP3 and currently implemented in LAPACK’s xgeqp3 routine. We show that the resulting algorithm, named QRDM, has similar rank-revealing properties of QP3 and better execution times. We present experimental results on a wide data set of numerically singular matrices, which has become a reference in the recent literature
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