Joint time-frequency representation of simulated earthquake accelerograms via the adaptive chirplet transform

Seismic accelerograms are inherently nonstationary signals since both the intensity and frequency content of seismic events evolve in time. The adaptive chirplet transform is a signal processing technique for joint time-frequency representation of nonstationary data. Analysis of a signal via the adaptive chirplet decomposition in conjunction with the Wigner-Ville distribution yields the so-called adaptive spectrogram which constitutes a valid representation of the signal in the time-frequency plane. In this paper the potential of this technique for capturing the temporal evolution of the frequency content of strong ground motions is assessed. In this regard, simulated nonstationary earthquake accelerograms compatible with an exponentially modulated and appropriately filtered Kanai-Tajimi spectrum are processed using the adaptive chirplet transform. These are samples of a random process whose evolutionary power spectrum can be represented by an analytical expression. It is suggested that the average of the ensemble of the adaptive chirplet spectrograms can be construed as an estimate of the underlying evolutionary power spectrum. The obtained numerical results show, indeed, that the estimated evolutionary power spectrum is in a good agreement with the one defined analytically. This fact points out the potential of the adaptive chirplet analysis for as a tool for capturing localized frequency content of arbitrary data- banks of real seismic accelerograms

Computer model calibration with large non-stationary spatial outputs: application to the calibration of a climate model

Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome this challenge, we employ a basis representation of the model outputs and observations: we match these decompositions to carry out the calibration efficiently. In the second step, we incorporate the non-stationary behaviour, in terms of spatial variations of both variance and correlations, in the calibration. We insert two integrated nested Laplace approximation-stochastic partial differential equation parameters into the calibration. A synthetic example and a climate model illustration highlight the benefits of our approach

Modeling and interpolation of the ambient magnetic field by Gaussian processes

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by imposing a Gaussian process (GP) prior on the latent scalar potential of the magnetic field. By rewriting the GP model in terms of a Hilbert space representation, we circumvent the computational pitfalls associated with GP modeling and provide a computationally efficient and physically justified modeling tool for the ambient magnetic field. The model allows for sequential updating of the estimate and time-dependent changes in the magnetic field. The model is shown to work well in practice in different applications: we demonstrate mapping of the magnetic field both with an inexpensive Raspberry Pi powered robot and on foot using a standard smartphone.Comment: 17 pages, 12 figures, to appear in IEEE Transactions on Robotic